Solve the problem.
-The function $f ( x ) = 1 + 1.6 \ln ( x + 1 )$ 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 8 consecutive free throws?
A) 78 days
B) 80 days
C) 276 days
D) 278 days

Question

Quizplus · Accepted Answer

The correct answer is A.The function $f ( x ) = 1 + 1.6 \ln ( x + 1 )$ 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.To find after how many days of practice the basketball player can make an average of 8 consecutive free throws, we need to solve the equation $f ( x ) = 8$.$1 + 1.6 \ln ( x + 1 ) = 8$$1.6 \ln ( x + 1 ) = 7$$\ln ( x + 1 ) = \frac{7}{1.6} \approx 4.375$$x + 1 = e^{\frac{7}{1.6}} \approx 78.39$$x \approx 78$Therefore, after about 78 days of practice, the basketball player can make an average of 8 consecutive free throws.

Solve the Problem f(x)=1+1.6ln⁡(x+1)f ( x ) = 1 + 1.6 \ln ( x + 1 )f(x)=1+1.6ln(x+1)

Solve the Problem $f ( x ) = 1 + 1.6 \ln ( x + 1 )$