Question

Question

The table below gives the value of a hypothetical $10,000 investment in a certain money market fund. Use a calculator or a
spreadsheet program to find an exponential regression model of the formy - ab' for the data set, and use it to estimate
the value of the investment 12 years after purchase.
Time (years) Value of Investment (USD)
0
10,000
1
11,000
2
12, 100
3
13,310
4
14,641
5
16,105,1
6
17,715.61

Answer 1

$31,384.28

Explanation:

If you're familiar with Pascal's triangle, you probably recognize the digits of the given values match successive lines of that triangle. This immediately suggests that the base of the exponential function is exactly 1.1, and the model can be written immediately as ...

y = 10000(1.1^x)

For x=12, the value of the investment is predicted to be ...

y = 10,000(1.1^12) ≈ 31,384.28

The value of the investment 12 years after purchase is predicted to be $31,384.28.

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In any event, a graphing calculator or spreadsheet can deduce the model for you. The attached calculator output shows it to be as described above.