Question

22. Use your model to determine when the volume of oil will get down to 500 gallons.

The table below shows the number of members (vl of a new sports website, with t being the number
of months the website has been open.
Months (t)
Members (y)
4
6
8
10
60 76 110 154
12
2221
23. Use your calculator to find a best-fit exponential regression model for the data.
24. According to the regression model, what is the rate of change?
25. What does your model predict the membership will be after 2 years (Hint: 24 months)?

Answer 1

21. y = 75000·0.935^t

22. after 74.6 days

23. y = 27.8112·1.18832^t

24. 18.8% per month

25. 1748

Explanation:

22. It is convenient to use the graphing calculator to solve this problem. The number of days is where the exponential curve has the value 500. It is about 74.55 days. (see the first attachment)

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23. y = 27.8112·1.18832^t (see the second attachment)

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24. The rate of change is the difference between the base of the exponential and 1, often expressed as a percentage. The time period is the units of t.

(1.18832 -1) × 100% ≈ 18.8% . . . . per month

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25. Evaluating the function for t=24 gives y ≈ 1748.30425259 ≈ 1748.

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Comment on graphing calculator

A graphing calculator can make very short work of problems like these. It is worthwhile to get to know how to use one well.