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Question 1207185: Mrs. Robinson made the table below showing the yearly balance of her savings
account. Interest on the account compounds annually. Which of the following
describes the best model to be used for Mrs. Robinson’s data?
Year Balance in Dollars
0 $400
5 $463.71
10 $537.57
15 $623.19
20 $722.44
25 $837.51
A) a positive linear function
B) a positive quadratic function
C) an exponential growth function
D) a positive absolute value function
Found 2 solutions by math_tutor2020, ikleyn:
Answer by math_tutor2020(3816)   (Show Source):
You can put this solution on YOUR website!
Use technology of your choice to determine these regression equations- linear: f(x) = 17.4249142857x + 379.5919047619
- quadratic: g(x) = 0.2559714286x^2 + 11.0256285714x + 400.9228571429
- exponential: h(x) = 400.0011431092e^(0.0295586331x)
The decimal values are approximate.
The 'e' is a special constant roughly equal to 2.718
h(x) is roughly equivalent to 400.0011431092*1.0299998258^x
From here, use spreadsheet software to construct the following table
| Given | Absolute Error | | x | y | linear | quadratic | exponential | | 0 | 400 | 20.408095 | 0.922857 | 0.001143 | | 5 | 463.71 | 3.006476 | 1.259714 | 0.000563 | | 10 | 537.57 | 16.271048 | 0.793714 | 0.002821 | | 15 | 623.19 | 17.775619 | 0.710857 | 0.002834 | | 20 | 722.44 | 5.65019 | 1.384 | 0.004115 | | 25 | 837.51 | 22.295238 | 0.964286 | 0.000024 |
The first two columns are copy/pasted from the table your teacher gave you. Except of course the dollar sign symbols have been erased.
The remaining 3 columns represent the absolute error when subtracting the stated y value from each regression output.
For example, when x = 0 the y value is y = 400.
If you plugged x = 0 into the linear regression function, then you should find f(0) = 379.5919047619
The error is approximately |y-f(x)| = |y-f(0)| = |400-379.5919047619| = 20.4080952381
Follow similar steps to compute the other error values.
In a perfect world, the error would be 0. But of course nothing is ever perfect.
The next best thing is to try to get as close to 0 as possible.
This occurs with the exponential regression function.
Therefore, the exponential is the best fit.
Answer: choice C
Answer by ikleyn(52776)  (Show Source):
You can put this solution on YOUR website! .
Notice that the years in the table are given with the constant step of 5 years.
From your table, calculate the ratio of the next term balance to the previous term balance.
I did it and obtained a constant value of 1.1592 (rounded) for all adjacent terms.
The fact that the consecutive fractions have constant values tells that the function is exponential.
That's all.
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As an additional clue, you may use the fact that banks use
either linear function (simple percent account) or exponential functions (compounded accounts).
They never use quadratic functions or absolute value functions as growth functions,
so for you in this problem the choice is, actually, between linear and exponential, only.
There is no any need to inflate this bubble to incredible proportions.
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