A school enrolls 500 students, and enrollment is estimated to grow 4% each year, so the roll after n years is P_n = 500(1.04)^n. About how many students are enrolled five years from now?

1. Growth by a fixed percentage is geometric, with common ratio 1.04 per year. 2. The model with a starting value uses P_n = P_0 r^n, so substitute n = 5. 3. Compute the growth factor: 1.04^5 = 1.04 x 1.04 x 1.04 x 1.04 x 1.04. 4. Step by step: 1.0816, then 1.1249, then 1.1699, then 1.2167. 5. Multiply by the starting roll: 500 x 1.2167 = 608.3 students. 6. Rounding gives about 608 students after five years. 7. Option A, 600, treats the growth as a flat 4% of 500 added five times, which is arithmetic, not geometric. 8. Option B applies only one year of growth, and option D compounds for roughly six years instead of five. _Source: OpenStax Algebra and Trigonometry (CC BY 4.0), Ch 13 "Sequences, Probability and Counting Theory", section 13.3 GEOMETRIC SEQUENCES_