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?

A. 472 days
B. 470 days
C. 102 days
D. 100 days

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.

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AliciaAugello AliciaAugello · Answer 2 · 2024-10-31T18:50:43-04:00

Final answer:

After approximately 98 days of practice, the basketball player can make an average of 7 consecutive free throws.

Explanation:

To find the number of days of practice after which the basketball player can make an average of 7 consecutive free throws, we need to solve the equation 7 = 1 + 1.3 ln(x + 1) for x.

First, subtract 1 from both sides of the equation: 6 = 1.3 ln(x + 1).

Next, divide both sides of the equation by 1.3: 4.6154 ≈ ln(x + 1).

To get rid of the natural logarithm, we can exponentiate both sides of the equation: e^(4.6154) ≈ x + 1.

Subtract 1 from both sides of the equation: e^(4.6154) - 1 ≈ x.

Approximately, x ≈ 98 days.

Learn more about Solution of equations with natural logarithms here:

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