Question 6 (2 points)
The University of McMaster undergraduate program is growing at a rate of $3 \%$ each year. The current enrollment is 12400 . Determine when the enrollment will reach 13250.

Step 1 ：Given that the University of McMaster undergraduate program is growing at a rate of 3% each year and the current enrollment is 12400, we are asked to determine when the enrollment will reach 13250.

Step 2 ：This is a problem of exponential growth. The formula for exponential growth is: \[A = P(1 + r)^t\] where: A is the amount of money accumulated after n years, including interest, P is the principal amount (the initial amount of money), r is the annual interest rate (in decimal), and t is the time in years.

Step 3 ：In this case, we want to find t when A = 13250, P = 12400, and r = 0.03.

Step 4 ：We can rearrange the formula to solve for t: \[t = \frac{\log(A/P)}{\log(1 + r)}\]

Step 5 ：Substituting the given values into the formula, we get: A = 13250, P = 12400, r = 0.03, and t = 2.2430232212878694.

Step 6 ：Final Answer: The enrollment will reach 13250 in approximately \(\boxed{2.24}\) years.