1. The annual revenue of the fitness cycling company Peloton in millions of dollars can be modeled by the equation P(t)=170(2.35)' where t represents the years since 2016. What is the growth factor? а. What is the annual growth/decay rate in percent? b. Algebraically determine in which year the annual revenue of Peloton will reach 900 million dollars. с. ()) *100- An advertising agency conducted a survey and found that the number of units sold, N , depends on the amount a, spent on advertising (in dollars). The following table gives the amount spent on advertising and the number of units sold accordingly. Source: The Nature of Mathematics, 10e, Smith, K.J. 3. Amount Spent (S) Number of Units Sold 3,572 3,902 4,055 1000 2 3000 5000 4,156 7000 Using a calculator, make a scatter plot of the data, where x represents the amount of money spent. Using your calculator, find the logarithmic regression (LnReg) that models this situation. Call this equation N(a), and round values to the nearest whole number. а. M0 According to the model N(a), how many units are sold if $8,000 is spent on advertising? b. Using the model N(a), algebraically determine how much money needs to be spent on advertising in order to sell 5,000 units. You may check your answer graphically. с. Fall 2019 350

Question
1.
The annual revenue of the fitness cycling company Peloton in millions of dollars can be modeled by the
equation P(t)=170(2.35)' where t represents the years since 2016.
What is the growth factor?
а.
What is the annual growth/decay rate in percent?
b.
Algebraically determine in which year the annual revenue of Peloton will reach 900 million dollars.
с.
())
*100-
An advertising agency conducted a survey and found that the number of units sold, N , depends on
the amount a, spent on advertising (in dollars). The following table gives the amount spent on
advertising and the number of units sold accordingly. Source: The Nature of Mathematics, 10e, Smith, K.J.
3.
Amount Spent (S)
Number of Units Sold
3,572
3,902
4,055
1000
2
3000
5000
4,156
7000
Using a calculator, make a scatter plot of the data, where x represents the amount of money spent.
Using your calculator, find the logarithmic regression (LnReg) that models this situation. Call this
equation N(a), and round values to the nearest whole number.
а.
M0
According to the model N(a), how many units are sold if $8,000 is spent on advertising?
b.
Using the model N(a), algebraically determine how much money needs to be spent on advertising in
order to sell 5,000 units. You may check your answer graphically.
с.
Fall 2019
350

Image Transcription

1. The annual revenue of the fitness cycling company Peloton in millions of dollars can be modeled by the equation P(t)=170(2.35)' where t represents the years since 2016. What is the growth factor? а. What is the annual growth/decay rate in percent? b. Algebraically determine in which year the annual revenue of Peloton will reach 900 million dollars. с. ()) *100- An advertising agency conducted a survey and found that the number of units sold, N , depends on the amount a, spent on advertising (in dollars). The following table gives the amount spent on advertising and the number of units sold accordingly. Source: The Nature of Mathematics, 10e, Smith, K.J. 3. Amount Spent (S) Number of Units Sold 3,572 3,902 4,055 1000 2 3000 5000 4,156 7000 Using a calculator, make a scatter plot of the data, where x represents the amount of money spent. Using your calculator, find the logarithmic regression (LnReg) that models this situation. Call this equation N(a), and round values to the nearest whole number. а. M0 According to the model N(a), how many units are sold if $8,000 is spent on advertising? b. Using the model N(a), algebraically determine how much money needs to be spent on advertising in order to sell 5,000 units. You may check your answer graphically. с. Fall 2019 350

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