Solve the problem.
-The function $f ( x ) = 1 + 1.5 \ln ( x + 1 )$ 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 6 consecutive free throws?
A) 27 days
B) 29 days
C) 105 days
D) 107 days

Question

Quizplus · Accepted Answer

The correct answer is A.Explanation:To solve this problem, we need to set $f(x) = 6$ and solve for $x$.$$6 = 1 + 1.5\ln(x + 1)$$$$5 = 1.5\ln(x + 1)$$$$\frac{5}{1.5} = \ln(x + 1)$$$$x + 1 = e^{\frac{5}{1.5}}$$$$x = e^{\frac{5}{1.5}} - 1$$$$x \approx 27$$Therefore, the basketball player can make an average of 6 consecutive free throws after about 27 days of practice.

Solve the Problem f(x)=1+1.5ln⁡(x+1)f ( x ) = 1 + 1.5 \ln ( x + 1 )f(x)=1+1.5ln(x+1)

Solve the Problem $f ( x ) = 1 + 1.5 \ln ( x + 1 )$