Question

The functions f(x) and g(x) in the table below show Max’s and Tommy’s savings respectively, in dollars, after x days, Some values are missing in the table.

Which statement best describes Max and Tommy’s savings in the long run?

A: The savings will increase by the same factor for both.

B: The savings will increase by the same amount for both.

C: Max will save more that tommy.

D: Tommy will save more than Max.

Answer 1

Exponential functions increase much faster than linear functions. We can see this clearly if we plug in some values. Let's go a couple of values of x ahead of the given values.

If x = 3, g(x) = 25. On the other hand, x = 3, f(x) = 27. 
If x = 4, g(x) = 35. On the other hand, x = 3, f(x) = 81. 

Therefore, since Max's savings are represented by f(x), his savings obviously grow much faster. Thus, the answer is C, Max will save more that tommy.