Question

A team of scientists estimate the current number of butterflies in a park to be 20 thousand. The butterfly population is expected to increase at a rate of 4% per year. Which equation models the number of butterflies, in thousands, in the park after n years? A. 0.04(20)n B. 20(1.04)n C. 1.04(20)n D. 20(0.04)n

Answer 1

The answer is C

Step-by-step explanation:

Answer 2

Option B is the correct answer.

Step-by-step explanation:

Current number of butterflies in the park = 20 thousand.

Rate of increase of butterfly population = 4% = 0.04

The population of butterfly after 1 year = 20+0.04*20 = 20*1.04

The population of butterfly after 2 years = 20*1.04 + 20*1.04*0.04 = 20*1.04*1.04

The population of butterfly after 3 years = 20*1.04*1.04 + 20*1.04*1.04*0.04 = 20*1.04*1.04*1.04

So, population of butterfly after n years = 20*(1.04*1.04*1.04* .... n times)

`= 20*1.04^n`

Option B is the correct answer.