The size of a certain insect population is given by P(t) = 400e.It, where t is measured in days. At what time will the population equal 2400? It will take days for the population to equal 2400. (Round to one decimal place as needed.)22. The rumor "People who study math all get scholarships" spreads within a technical high school. Data in the following table show the number of students N who have heard the rumor after t days. Time, t (in days) 3 4 5 6 7 8 9 10 11 12 Number, N, Who Have Heard the Rumor 1 2 3 4 9 15 21 23 25 25 26 27 a) Use regression to fit a logistic equation N(t) = = _ to the data. 1 tae - bt N(t) 1+ (Round to three decimal places as needed.) b) Estimate the limiting value of the function. At most, how many students will hear the rumor? According to the logistic equation, at most students will hear the rumor. (Round to the nearest whole number as needed.) c) Graph the function. Choose the correct graph below. Each viewing window has a horizontal axis from 0 to 13 in increments of 1 and a vertical axis from 0 to 31 In increments of 5 O A. O B O c. a a Q d) Find the rate of change, N'(1). Use the rounded values from part a) for your calculations. N'(t) = (Type an exact answer in terms of c. Use integers or decimals for any numbers in the equation. Round to three decimal places as needed.) e) Find lim N'(t), and explain its meaning- 1-+00 lim N'(1) = t-+ 0o (Round to the nearest integer as needed.) What does the value of lim N'(t) mean? O A. After a very long time, the number of students who heard the rumor will remain constant. O B. Eventually, everyone will have heard the rumor. O C. The number of students who heard the rumor will increase faster and faster. O D. As time goes by, the number of students who heard the rumor will be 0