Question

The function f(x) = 1 + 1.3 In (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?

Answer 1

To find out after how many days of practice the player can make an average of 8 consecutive free throws, we need to solve the equation 1 + 1.3 In (x + 1) = 8. The solution is x = e^(7/1.3) - 2.

Step-by-step explanation:

The function f(x) = 1 + 1.3 In (x + 1) models the average number of free-throws a basketball player can make consecutively during practice as a function of time.

To find out after how many days of practice the player can make an average of 8 consecutive free throws, we need to solve the equation 1 + 1.3 In (x + 1) = 8.

First, subtract 1 from both sides of the equation: 1.3 In (x + 1) = 7.

Next, divide both sides of the equation by 1.3: In (x + 1) = 7/1.3.

Finally, take the natural logarithm of both sides of the equation to solve for x: x + 1 = e^(7/1.3) - 1.

Subtract 1 from both sides to get the final answer: x = e^(7/1.3) - 2.