Question

The functions f(x) and g(x) in the table below show Kim's and Ben's savings respectively, in dollars, after x days. Some values are missing in the table.
x(years) 1 2 3
g(x) = 3x
Kim's savings in dollars 3 9
f(x) = 3x + 5
Ben's savings in dollars 8 11


Which statement best describes Kim and Ben's savings in the long run?
The savings will increase by the same factor for both.
The savings will increase by the same amount for both.
Kim will save more than Ben.
Ben will save more than Kim.


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Answer 1

The table can be filled in as follows:

$\begin{array}{r|cccc}x(days)&1&2&3&4\\g(x)=3^x&3&9&27&81\\f(x)=3x+5&8&11&14&17\end{array}$

After 3 days, Kim's savings already exceeds Ben's, and is increasing at a faster rate. The appropriate descriptor is ...

... Kim will save more than Ben

_____

An exponential function increases faster than any polynomial function. (A linear function is a polynomial function.)

If Kim keeps up her savings for 28 days, her account balance will exceed the US Gross National Product of more than $20 trilliion. (Exponential functions tend to increase very rapidly!) Meanwhile, Ben's savings will be $89 on day 28.

_____

Please note the discrepancy in the problem statement. The verbiage says "days", but the table shows "years".

Answer 2

Answer:

(C)  Kim will save more than Ben.

Step-by-step explanation:

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