The formula y=1+1.4ln(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 5 consecutive free throws?
To find after how many days of practice the basketball player can make an average of 5 consecutive free throws, we need to solve the equation y = 5, where y is given by the formula y = 1 + 1.4ln(x + 1).
Step 1: Set up the equation:
1 + 1.4ln(x + 1) = 5
Step 2: Subtract 1 from both sides:
1.4ln(x + 1) = 4
Step 3: Divide both sides by 1.4:
ln(x + 1) = 2.8571
Step 4: Rewrite the equation in exponential form:
e^(ln(x + 1)) = e^2.8571
Step 5: Simplify:
x + 1 = e^2.8571
Step 6: Subtract 1 from both sides:
x = e^2.8571 - 1
Step 7: Use a calculator to find the approximate value:
x ≈ 16.43
Therefore, after approximately 16.43 days of practice, the basketball player can make an average of 5 consecutive free throws.