The population of Whoville has been increasing at a rate of 0.8% per year since 2001. If the population was 13,500 at the beginning of 2015, which expression gives its population at the end of 2009?

Question

A- 13,500(0.992)^6

B- 13,500(1.008)^−6

C- 13,500(1.008)^6

D- 13,500(0.992)^−6

Answer 1

Start with the exponential growth equation:

P(t) = P₀·(1+rate)^t

1. P(t) = population in year t = 13,500 in 2015
2. P₀ = starting population (in 2009)
3. rate = growth rate in decimal form = 0.008
4. t = years since 2009 = 2015 - 2009 = 6

Now fill in the numbers:

P(t) = P₀·(1+rate)^t

13,500 = P₀ (1 + 0.008)⁶

Solve for P₀.