Question

The function E ( t ) = P ( 1 + r ) t models the enrollment at Hamilton College t years from now, where P is the present number of students enrolled and r is the annual rate of increase in enrollment. The college's office of advancement projects that enrollment will increase 2.5% annually and that there will be 13,916 students enrolled at Hamilton 6 years from now. Based on the model, approximately how many students are presently enrolled at Hamilton College? 4,000 8,000 12,000 16,000

Answer 1

Approximately 12,000 students are presently enrolled at Hamilton College, calculated by solving the given exponential growth function for the present number of students with a 2.5% annual growth rate over 6 years with the future enrollment set at 13,916 students.

Step-by-step explanation:

The student is asking how to determine the present enrollment at Hamilton College given the future enrollment after 6 years and the annual rate of increase.

To find the present number of students (P), we can use the given function E(t) = P(1 + r)^t. We know that E(6) = 13,916 students, r = 2.5% or 0.025 as a decimal, and t = 6 years. Now, we can solve for P.

First, we plug the given values into the model:
E(6) = P(1 + 0.025)^6

13,916 = P(1.025)^6

13,916 = P * 1.159274

P = 13,916 / 1.159274

P ≈ 12,000

Therefore, approximately 12,000 students are presently enrolled at Hamilton College.