Please help me solve this word problem

Question

The population of a colony of a certain insect obeys the law of uninhibited growth. If there are 500 insects initially and there are 800 after one day, what is the size of the colony after 3 days?

Answer 1

The formula for uninhibited growth:

 

A_t = A₀e^kt, where A₀ = starting amount, e = Euler's constant, k = rate of growth, t = time.

 

800 = 500e^k

1.6 = e^k

ln 1.6 = k

0.47 = k

 

A₃ = 500e^(0.47)3

A₃ = 500e^1.41

A₃ = 500(4.1)

A₃ = 2048