According to a study about a particular mathematics course t

According to a study about a particular mathematics course, the relation between the total amount of time students spend studying material for a test and their test grade can be modeled by the function T(x) = 21 + 25 ln(x + 1), where x represents the amount of time spent studying, in hours(0 lessthanorequalto x lessthanorequalto 23). a. What should be the test grade of a student who has spent 3 hours studying? b. Find the expression for T^-1(x). c. Evaluate T^-1(100). In a sentence, explain what your result means in this situation.

Solution

a. given x = 3

T(x) = 21+25ln(x+1)

T(3) = 21+25ln4

T(3) = 21+25x1.39 = 21+34.75 = 55.75

(b). Let T(x) =y

then y-21 = 25ln(x+1)

(y-21)/25 = ln(x+1)

e^(y-21)/25-1 = x

T^-1(x) = e^(y-21)/25-1

T^-1(100) = e^(100-21)/25-1

T^-1(100) = e^(79)/25-1 = 23.57-1 = 22.57

This result mean if he get grade 100 then the number of hour that he has to study is 22.57 hours.