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How to complete a table of values of an exponential function? [closed]
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I got this question from my teacher and I tried to solve but no luck!
the question given is:
Toss 100 pennies and remove all of the ‘heads’. Toss the remaining
pennies, and again, remove all heads. Repeat this process until all
coins have been removed.
A. Record the number of pennies tossed for each trial in a table.
beginarray
hline
textNumber of trial & textNumber of pennies tossed \
hline
1 & 100 \
2 & \
3 & \
4 & \
5 & \
6 & \
7 & \
8 & \
9 & \
10 & \
hline
endarray
B. Graph the data and draw a smooth curve through the points.
C. Explain why this data can be modeled by an exponential function.
Based on what I know, we should use the general form of an exponential function which is $y=acdot b^x + c$
I think C, in this case, is 100
and from the pattern, we can divide the second value of Y by the first value of Y then we get the common ratio that can help to complete the table of value.
In this question, I have only one Y-value!
probability exponential-function exponential-distribution
edited Jul 18 at 2:22
mvw
30.5k22250
asked Jul 18 at 1:33
MOHAIMEN AHMED
102
closed as off-topic by amWhy, Y. Forman, Anonymous, max_zorn, Rhys Steele Jul 18 at 6:36
This question appears to be off-topic. The users who voted to close gave these specific reasons:
- "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – amWhy, Rhys Steele
- "This question is not about mathematics, within the scope defined in the help center." – Y. Forman, Anonymous, max_zorn
add a comment |Â
up vote
1
down vote
favorite
I got this question from my teacher and I tried to solve but no luck!
the question given is:
Toss 100 pennies and remove all of the ‘heads’. Toss the remaining
pennies, and again, remove all heads. Repeat this process until all
coins have been removed.
A. Record the number of pennies tossed for each trial in a table.
beginarray
hline
textNumber of trial & textNumber of pennies tossed \
hline
1 & 100 \
2 & \
3 & \
4 & \
5 & \
6 & \
7 & \
8 & \
9 & \
10 & \
hline
endarray
B. Graph the data and draw a smooth curve through the points.
C. Explain why this data can be modeled by an exponential function.
Based on what I know, we should use the general form of an exponential function which is $y=acdot b^x + c$
I think C, in this case, is 100
and from the pattern, we can divide the second value of Y by the first value of Y then we get the common ratio that can help to complete the table of value.
In this question, I have only one Y-value!
probability exponential-function exponential-distribution
edited Jul 18 at 2:22
mvw
30.5k22250
asked Jul 18 at 1:33
MOHAIMEN AHMED
102
closed as off-topic by amWhy, Y. Forman, Anonymous, max_zorn, Rhys Steele Jul 18 at 6:36
This question appears to be off-topic. The users who voted to close gave these specific reasons:
- "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – amWhy, Rhys Steele
- "This question is not about mathematics, within the scope defined in the help center." – Y. Forman, Anonymous, max_zorn
It seems (from your transcription of the assignment) that the table of values should be completed by experiment, not by mathematical reasoning...
– Y. Forman
Jul 18 at 1:39
2
At each step in the process, we should expect that the amount will approximately be halved. I would expect it to act much more like $100(frac12)^n$. You should be able to convince yourself of this using an argument related to expected value. (To see the expected number of coins remaining after the second flip for example, pretend that we begin with 100 coins and flip each coin twice in succession, regardless of whether or not a head was flipped. Keep only the coins that flipped tails twice in a row).
– JMoravitz
Jul 18 at 1:54
add a comment |Â
up vote
1
down vote
favorite
up vote
1
down vote
favorite
I got this question from my teacher and I tried to solve but no luck!
the question given is:
Toss 100 pennies and remove all of the ‘heads’. Toss the remaining
pennies, and again, remove all heads. Repeat this process until all
coins have been removed.
A. Record the number of pennies tossed for each trial in a table.
beginarray
hline
textNumber of trial & textNumber of pennies tossed \
hline
1 & 100 \
2 & \
3 & \
4 & \
5 & \
6 & \
7 & \
8 & \
9 & \
10 & \
hline
endarray
B. Graph the data and draw a smooth curve through the points.
C. Explain why this data can be modeled by an exponential function.
Based on what I know, we should use the general form of an exponential function which is $y=acdot b^x + c$
I think C, in this case, is 100
and from the pattern, we can divide the second value of Y by the first value of Y then we get the common ratio that can help to complete the table of value.
In this question, I have only one Y-value!
probability exponential-function exponential-distribution
edited Jul 18 at 2:22
mvw
30.5k22250
asked Jul 18 at 1:33
MOHAIMEN AHMED
102
I got this question from my teacher and I tried to solve but no luck!
the question given is:
Toss 100 pennies and remove all of the ‘heads’. Toss the remaining
pennies, and again, remove all heads. Repeat this process until all
coins have been removed.
A. Record the number of pennies tossed for each trial in a table.
beginarray
hline
textNumber of trial & textNumber of pennies tossed \
hline
1 & 100 \
2 & \
3 & \
4 & \
5 & \
6 & \
7 & \
8 & \
9 & \
10 & \
hline
endarray
B. Graph the data and draw a smooth curve through the points.
C. Explain why this data can be modeled by an exponential function.
Based on what I know, we should use the general form of an exponential function which is $y=acdot b^x + c$
I think C, in this case, is 100
and from the pattern, we can divide the second value of Y by the first value of Y then we get the common ratio that can help to complete the table of value.
In this question, I have only one Y-value!
probability exponential-function exponential-distribution
edited Jul 18 at 2:22
mvw
30.5k22250
asked Jul 18 at 1:33
MOHAIMEN AHMED
102
edited Jul 18 at 2:22
mvw
30.5k22250
edited Jul 18 at 2:22
mvw
30.5k22250
edited Jul 18 at 2:22
mvw
30.5k22250
30.5k22250
asked Jul 18 at 1:33
MOHAIMEN AHMED
102
asked Jul 18 at 1:33
MOHAIMEN AHMED
102
asked Jul 18 at 1:33
MOHAIMEN AHMED
102
102
closed as off-topic by amWhy, Y. Forman, Anonymous, max_zorn, Rhys Steele Jul 18 at 6:36
This question appears to be off-topic. The users who voted to close gave these specific reasons:
- "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – amWhy, Rhys Steele
- "This question is not about mathematics, within the scope defined in the help center." – Y. Forman, Anonymous, max_zorn
closed as off-topic by amWhy, Y. Forman, Anonymous, max_zorn, Rhys Steele Jul 18 at 6:36
This question appears to be off-topic. The users who voted to close gave these specific reasons:
- "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – amWhy, Rhys Steele
- "This question is not about mathematics, within the scope defined in the help center." – Y. Forman, Anonymous, max_zorn
It seems (from your transcription of the assignment) that the table of values should be completed by experiment, not by mathematical reasoning...
– Y. Forman
Jul 18 at 1:39
2
At each step in the process, we should expect that the amount will approximately be halved. I would expect it to act much more like $100(frac12)^n$. You should be able to convince yourself of this using an argument related to expected value. (To see the expected number of coins remaining after the second flip for example, pretend that we begin with 100 coins and flip each coin twice in succession, regardless of whether or not a head was flipped. Keep only the coins that flipped tails twice in a row).
– JMoravitz
Jul 18 at 1:54
add a comment |Â
It seems (from your transcription of the assignment) that the table of values should be completed by experiment, not by mathematical reasoning...
– Y. Forman
Jul 18 at 1:39
2
At each step in the process, we should expect that the amount will approximately be halved. I would expect it to act much more like $100(frac12)^n$. You should be able to convince yourself of this using an argument related to expected value. (To see the expected number of coins remaining after the second flip for example, pretend that we begin with 100 coins and flip each coin twice in succession, regardless of whether or not a head was flipped. Keep only the coins that flipped tails twice in a row).
– JMoravitz
Jul 18 at 1:54
It seems (from your transcription of the assignment) that the table of values should be completed by experiment, not by mathematical reasoning...
– Y. Forman
Jul 18 at 1:39
It seems (from your transcription of the assignment) that the table of values should be completed by experiment, not by mathematical reasoning...
– Y. Forman
Jul 18 at 1:39
2
2
At each step in the process, we should expect that the amount will approximately be halved. I would expect it to act much more like $100(frac12)^n$. You should be able to convince yourself of this using an argument related to expected value. (To see the expected number of coins remaining after the second flip for example, pretend that we begin with 100 coins and flip each coin twice in succession, regardless of whether or not a head was flipped. Keep only the coins that flipped tails twice in a row).
– JMoravitz
Jul 18 at 1:54
At each step in the process, we should expect that the amount will approximately be halved. I would expect it to act much more like $100(frac12)^n$. You should be able to convince yourself of this using an argument related to expected value. (To see the expected number of coins remaining after the second flip for example, pretend that we begin with 100 coins and flip each coin twice in succession, regardless of whether or not a head was flipped. Keep only the coins that flipped tails twice in a row).
– JMoravitz
Jul 18 at 1:54
add a comment |Â
2 Answers
2
active
oldest
votes
up vote
1
down vote
accepted
The word "record" means that you should observe what happens and write it down, not try to predict it. Indeed, notice that there isn't any way to predict the first new value - you can't predict how many pennies will come down heads unless you try it and see!
The problem seems to be literally asking you to flip 100 pennies, remove the ones that come up heads, and repeat, writing down the results as you go.
answered Jul 18 at 1:47
Reese
14.3k11135
add a comment |Â
up vote
0
down vote
Why not follow the instructions?
This is a physical experiment, which includes documenting and analyzing your observations, fitting them to a mathematical model.
Your general function seems to be
$$
y(x) = a cdot b^x
$$
Think about using a half logarithmic plot ($x$ vs $log y$) so you can interpolate with a simple straight line.
answered Jul 18 at 2:20
mvw
30.5k22250
add a comment |Â
2 Answers
2
active
oldest
votes
2 Answers
2
active
oldest
votes
active
oldest
votes
active
oldest
votes
up vote
1
down vote
accepted
The word "record" means that you should observe what happens and write it down, not try to predict it. Indeed, notice that there isn't any way to predict the first new value - you can't predict how many pennies will come down heads unless you try it and see!
The problem seems to be literally asking you to flip 100 pennies, remove the ones that come up heads, and repeat, writing down the results as you go.
answered Jul 18 at 1:47
Reese
14.3k11135
add a comment |Â
up vote
1
down vote
accepted
The word "record" means that you should observe what happens and write it down, not try to predict it. Indeed, notice that there isn't any way to predict the first new value - you can't predict how many pennies will come down heads unless you try it and see!
The problem seems to be literally asking you to flip 100 pennies, remove the ones that come up heads, and repeat, writing down the results as you go.
answered Jul 18 at 1:47
Reese
14.3k11135
add a comment |Â
up vote
1
down vote
accepted
up vote
1
down vote
accepted
The word "record" means that you should observe what happens and write it down, not try to predict it. Indeed, notice that there isn't any way to predict the first new value - you can't predict how many pennies will come down heads unless you try it and see!
The problem seems to be literally asking you to flip 100 pennies, remove the ones that come up heads, and repeat, writing down the results as you go.
answered Jul 18 at 1:47
Reese
14.3k11135
The word "record" means that you should observe what happens and write it down, not try to predict it. Indeed, notice that there isn't any way to predict the first new value - you can't predict how many pennies will come down heads unless you try it and see!
The problem seems to be literally asking you to flip 100 pennies, remove the ones that come up heads, and repeat, writing down the results as you go.
answered Jul 18 at 1:47
Reese
14.3k11135
answered Jul 18 at 1:47
Reese
14.3k11135
answered Jul 18 at 1:47
Reese
14.3k11135
answered Jul 18 at 1:47
Reese
14.3k11135
14.3k11135
add a comment |Â
add a comment |Â
up vote
0
down vote
Why not follow the instructions?
This is a physical experiment, which includes documenting and analyzing your observations, fitting them to a mathematical model.
Your general function seems to be
$$
y(x) = a cdot b^x
$$
Think about using a half logarithmic plot ($x$ vs $log y$) so you can interpolate with a simple straight line.
answered Jul 18 at 2:20
mvw
30.5k22250
add a comment |Â
up vote
0
down vote
Why not follow the instructions?
This is a physical experiment, which includes documenting and analyzing your observations, fitting them to a mathematical model.
Your general function seems to be
$$
y(x) = a cdot b^x
$$
Think about using a half logarithmic plot ($x$ vs $log y$) so you can interpolate with a simple straight line.
answered Jul 18 at 2:20
mvw
30.5k22250
add a comment |Â
up vote
0
down vote
up vote
0
down vote
Why not follow the instructions?
This is a physical experiment, which includes documenting and analyzing your observations, fitting them to a mathematical model.
Your general function seems to be
$$
y(x) = a cdot b^x
$$
Think about using a half logarithmic plot ($x$ vs $log y$) so you can interpolate with a simple straight line.
answered Jul 18 at 2:20
mvw
30.5k22250
Why not follow the instructions?
This is a physical experiment, which includes documenting and analyzing your observations, fitting them to a mathematical model.
Your general function seems to be
$$
y(x) = a cdot b^x
$$
Think about using a half logarithmic plot ($x$ vs $log y$) so you can interpolate with a simple straight line.
answered Jul 18 at 2:20
mvw
30.5k22250
edited Jul 18 at 2:26
answered Jul 18 at 2:20
mvw
30.5k22250
answered Jul 18 at 2:20
mvw
30.5k22250
answered Jul 18 at 2:20
mvw
30.5k22250
30.5k22250
add a comment |Â
add a comment |Â
It seems (from your transcription of the assignment) that the table of values should be completed by experiment, not by mathematical reasoning...
– Y. Forman
Jul 18 at 1:39
2
At each step in the process, we should expect that the amount will approximately be halved. I would expect it to act much more like $100(frac12)^n$. You should be able to convince yourself of this using an argument related to expected value. (To see the expected number of coins remaining after the second flip for example, pretend that we begin with 100 coins and flip each coin twice in succession, regardless of whether or not a head was flipped. Keep only the coins that flipped tails twice in a row).
– JMoravitz
Jul 18 at 1:54