An instructor has determined that students' grads on the final exam depend on the amount of time, t, they spend studying for it and can be modeled by the formula g(t)=(21t+10)/(20t+45). Note that the function's output is a fraction or decimal which should then be converted to a percent to give the student's grade on the exam.

Question

-If the student were able to study as long as s/he desired, what score would s/he approach (but never actually reach)?

This is how I tried to solve this question:

Eliminate 10 and 45
g(t)---> 21/20=1.05

So would the answer be that the student would approach 105%? (but never actually reached)

Any help is greatly appreciated!

Answer 1

That is correct. You can see that at t=35, g(t) = 1

So, a student will likely get 100% if he spends 35 hours studying. I guess it's unlikely that more time than that will be spent...