Question

Biff observes that in every math test he has taken this year, he has scored 2 points higher than the previous test. His score on the first test was 56

Exponential models
Biff observes that in every math test he has taken this year, he has scored 2 points higher than the previous test. His score on the first test was 56. He models his test scores with the exponential function $$\displaystyle{s}{\left({n}\right)}={28}⋅{2}^{{n}}$$ where s(n) is the score on his nth test. Is this a reasonable model? Explain.

2021-05-08

Ene score of the first test Is 56. Each test score is 2 points higher than the previous test score. So the score of the second test is 56+ 2 = 58.
The score of the third test is 58+ 2= 60.
And so on.
The scores form an arithmetic sequence 56, 58, 60, ......... with common difference 2.
But the values of the given exponential function $$s(n)=28*2^n$$, describe a geometric sequence with common ratio 2.
So the exponential function cannot be used to model this problem.