Select the correct answer. A geneticist needs to grow a stock of fruit flies for her experiments. She currently has a stock of 200 fruit flies and predicts t 38% each day. Which function could she use to calculate f(n) the number of days required for her stock to grow to n fruit A. f(n)=log_(0.38)((n)/(200)) B. f(n)=log_(1.38)((n)/(200)) C. f(n)=log_(0.38)((200)/(n)) D. f(n)=log_(1.38)((200)/(n))

To solve this problem, we need to find the function that represents the number of days required for the stock of fruit flies to grow to n fruit flies.<br /><br />Given information:<br />- The stock of fruit flies currently has 200 fruit flies.<br />- The stock of fruit flies grows by 38% each day.<br /><br />Let's analyze the options:<br /><br />A. $f(n)=log_{0.38}(\frac {n}{200})$<br /> This option is incorrect because the base of the logarithm should be greater than 1, as the stock of fruit flies is growing.<br /><br />B. $f(n)=log_{1.38}(\frac {n}{200})$<br /> This option is correct. The base of the logarithm is 1.38, which represents the growth rate of 38%. The argument of the logarithm is $\frac{n}{200}$, which represents the ratio of the final number of fruit flies to the initial number of fruit flies.<br /><br />C. $f(n)=log_{0.38}(\frac {200}{n})$<br /> This option is incorrect because the base of the logarithm should be greater than 1, as the stock of fruit flies is growing.<br /><br />D. $f(n)=log_{1.38}(\frac {200}{n})$<br /> This option is incorrect because the argument of the logarithm should be the ratio of the final number of fruit flies to the initial number of fruit flies, which is $\frac{n}{200}$, not $\frac{200}{n}$.<br /><br />Therefore, the correct answer is option B: $f(n)=log_{1.38}(\frac {n}{200})$.