A population model is given by P(t) = 500(1.08)^t, where t is measured in years. Which value is closest to P(5)?

Substitute $t=5$ into the model: $P(5)=500(1.08)^5$. Since $1.08^2=1.1664$ and $1.08^4\approx1.3605$, we get $1.08^5\approx1.4693$, so $P(5)\approx500(1.4693)\approx734.7$, which is closest to $735$, choice H. Choice F ($540$) applies the 8\% growth once, $500(1.08)$, instead of raising the growth factor to the 5th power. Choice G ($700$) uses simple growth, $500(1+5\cdot0.08)=700$, which ignores compounding. Choice J ($800$) is too large; it would need a yearly growth factor close to $1.12$. Exponential growth compounds each year on the larger amount.