Question

Biff observes that in every math test he has taken this year, he has scored 4 points higher than the previous test. His score on his first test was 92. He models his test scores with the exponential function s(n) = 23 · 4n where s(n) is the score on his nth test. Is this a reasonable model ? Complete the explanation.
 

Answer 1

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.