Question

The function f(x) = 1 + 1.3 ln (x + 1) models the average number of free-throws a basketball player can make consecutively during practice as a function of time, where x is the number of consecutive days the basketball player has practiced for two hours. after how many days of practice can the basketball player make an average of 7 consecutive free throws? 472 days 470 days 102 days 100 days

Answer 1

F(x) = 1+1.3*ln(x+1). Plug in 7 for f(x) and reduce the equation: 7 = 1+1.3*ln(x+1) => 6/1.3=ln(x+1). This becomes e^(6/1.3)=x+1, and then 101.03 -1 = x. x = 100.03. Therefore, the basketball player can average 7 consecutive free throws after 100 days.