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Exponential Models
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Question #1
You open a bank account to save for college and deposit $400 in the account. Each year, the balance in
your account will increase 5%. a. Write a function that models your annual balance. b. What will be the
total amount in your account after 7 yr? Use the exponential function and extend the table to answer part
b.
Answer:
Years account Open Balance this Year Total Balance
0 $400 $400
1 $400(1.05) $420
2 $420(1.05) $441
3 $441(1.05) $463.05
4 $463.05(1.05) $486.20
5 $486.20(1.05) $510.51
6 $510.51(1.05) $536.04
7 $536.04(1.05) $562.84
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So, the total balance after 7 years is $562.84
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Question #2
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For the following exercises, use a graphing utility to create a scatter diagram of the data given in the
table. Observe the shape of the scatter diagram to determine whether the data is best described by an
exponential, logarithmic, or logistic model. Then use the appropriate regression feature to find an
equation that models the data. When necessary, round values to five decimal places.
x 0 0.5 1 1.5 2 3 4 5 6 7 8
f ( x) 2.2 2.9 3.9 4.8 6.4 9.3 12.3 15 16.2 17.3 17.9
Answer:
Step 1
Remember that regression analysis is the process of looking for a best fit of model for a set of data. This
can be done on a graphing utility as follows:
1. Press [STAT], the input corresponging x-values of data in L1, and y-values of data in L2.
2. Use [STATPLOT] to observe a scatterplot of the data.
3. Press [STAT], then [CALC] then [ExpReg]/[LnReg]/[Logistic].
This will show you a function in either the form of an exponential, a logarithmic or a logistic model.
4. Graph this equation on the same window as the scatterplot to see if it fits the data.
Step 2
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1. Press [STAT], the input corresponging x-values of data in L1, and y-values of data in L2.
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2. Use [STATPLOT] to observe a scatterplot of the data.
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Step 3
Based on the plots of the points, it can be exponential or logarithmic.
However, upon checking both regression analysis, the one with the closest value of 𝑟 2 to 1 is
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exponential, hence, its formula is 𝑦 = −0.68374𝑥 The graph of which is below:
1+7.54619𝑒
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Answer: 𝑦 =
1+7.54619𝑒 −0.68374𝑥
Question #3
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For the following exercises, use a graphing utility to create a scatter diagram of the data given in the
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table. Observe the shape of the scatter diagram to determine whether the data is best described by an
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uB Questions and Answers Sheet 1
Exponential Models
Ed
Question #1
You open a bank account to save for college and deposit $400 in the account. Each year, the balance in
your account will increase 5%. a. Write a function that models your annual balance. b. What will be the
total amount in your account after 7 yr? Use the exponential function and extend the table to answer part
b.
Answer:
Years account Open Balance this Year Total Balance
0 $400 $400
1 $400(1.05) $420
2 $420(1.05) $441
3 $441(1.05) $463.05
4 $463.05(1.05) $486.20
5 $486.20(1.05) $510.51
6 $510.51(1.05) $536.04
7 $536.04(1.05) $562.84
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So, the total balance after 7 years is $562.84
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Question #2
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For the following exercises, use a graphing utility to create a scatter diagram of the data given in the
table. Observe the shape of the scatter diagram to determine whether the data is best described by an
exponential, logarithmic, or logistic model. Then use the appropriate regression feature to find an
equation that models the data. When necessary, round values to five decimal places.
x 0 0.5 1 1.5 2 3 4 5 6 7 8
f ( x) 2.2 2.9 3.9 4.8 6.4 9.3 12.3 15 16.2 17.3 17.9
Answer:
Step 1
Remember that regression analysis is the process of looking for a best fit of model for a set of data. This
can be done on a graphing utility as follows:
1. Press [STAT], the input corresponging x-values of data in L1, and y-values of data in L2.
2. Use [STATPLOT] to observe a scatterplot of the data.
3. Press [STAT], then [CALC] then [ExpReg]/[LnReg]/[Logistic].
This will show you a function in either the form of an exponential, a logarithmic or a logistic model.
4. Graph this equation on the same window as the scatterplot to see if it fits the data.
Step 2
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1. Press [STAT], the input corresponging x-values of data in L1, and y-values of data in L2.
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2. Use [STATPLOT] to observe a scatterplot of the data.
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Step 3
Based on the plots of the points, it can be exponential or logarithmic.
However, upon checking both regression analysis, the one with the closest value of 𝑟 2 to 1 is
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18.41663
exponential, hence, its formula is 𝑦 = −0.68374𝑥 The graph of which is below:
1+7.54619𝑒
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Answer: 𝑦 =
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Question #3
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For the following exercises, use a graphing utility to create a scatter diagram of the data given in the
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table. Observe the shape of the scatter diagram to determine whether the data is best described by an
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exponential, logarithmic, or logistic model. Then use the appropriate regression feature to find an
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