The formula y=1+1.3ln(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 o consecutive days the basketbal player has practiced for two hours. After 46 days of practice, what is the average number of consecutive free-throws the basketball player makes? Round to the nearest whole number. A. 6 consecutive free-throws B. 10 consecutive free-throus C. 7 consecutive free-throws D. 9 consecutive free-throws

To find the average number of consecutive free-throws the basketball player makes after 46 days of practice, we need to substitute x = 46 into the given formula and solve for y.<br /><br />The formula is given as:<br />$y = 1 + 1.3\ln(x+1)$<br /><br />Substituting x = 46, we get:<br />$y = 1 + 1.3\ln(46+1)$<br />$y = 1 + 1.3\ln(47)$<br /><br />Now, we need to calculate the value of $\ln(47)$ and then multiply it by 1.3.<br /><br />Using a calculator, we find that $\ln(47) \approx 3.85$.<br /><br />Substituting this value into the equation, we get:<br />$y = 1 + 1.3(3.85)$<br />$y = 1 + 5.055$<br />$y \approx 6.055$<br /><br />Rounding to the nearest whole number, we get y = 6.<br /><br />Therefore, the average number of consecutive free-throws the basketball player makes after 46 days of practice is 6 consecutive free-throws.<br /><br />The correct answer is A. 6 consecutive free-throws.