The formula y=1+1.5ln(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 105 days of practice, what is the average number of consecutive free-throws the basketball player makes? Round to the nearest whole number. A. 12 consecutive free-throws B. 8 consecutive free -throws C. 11 consecutive free -throws D. 9 consecutive free-throws

the average number of consecutive free-throws the basketball player makes after 105 days of practice, we need to substitute x = 105 into the given formula and simplify.<br /><br />Given formula: $y = 1 + 1.5\ln(x+1)$<br /><br />Substitute x = 105:<br />$y = 1 + 1.5\ln(105+1)$<br />$y = 1 + 1.5\ln(106)$<br /><br />Now, we need to calculate the value of $\ln(106)$ and then multiply it by 1.5.<br /><br />Using a calculator, we find that $\ln(106) \approx 4.198$.<br /><br />Substitute this value into the equation:<br />$y = 1 + 1.5(4.198)$<br />$y = 1 + 6.297$<br />$y \approx 7.297$<br /><br />Rounding to the nearest whole number, we get y ≈ 7.<br /><br />Therefore, the average number of consecutive free-throws the basketball player makes after 105 days of practice is approximately 7.<br /><br />The correct answer is B. 8 consecutive free-throws.