A school has 284 students and its roll is estimated to grow 4% a year, modelled by P_n = 284 * 1.04^n. About how many students are there seven years later?

1. A 4% yearly rise means each year the roll is 104% of the year before, so the common ratio is 1.04. 2. The index n counts years after the starting year, so seven years later means n = 7. 3. Substituting gives P_7 = 284 * 1.04^7. 4. Raising 1.04 to the seventh power gives about 1.316. 5. Multiplying gives 284 times 1.316, which is about 374 students. 6. Treating the growth as simple rather than compound would add 4% of 284 seven times, giving about 364, and that is the trap here. 7. Rounding the ratio to 1.05 would overshoot to about 400, so the ratio must be kept exact. _Source: OpenStax Algebra and Trigonometry (CC BY 4.0), Ch 13 "Sequences, Probability and Counting Theory", section 13.3 Geometric Sequences_