Question

A population of insects doubles every 3 days. The population started with 8 insects. The function that models this growth is f(x)=8(2)^x/3. Evaluate the function over the domain {0,3,6,12}. Intercept the results and use a graph to explain your answer.

Answer 1

12 bbbbbbbbcccccccccccccccc

Answer 2

The evaluated function over the elements of the domain is:

f(0) = 8

f(3) = 16

f(6) = 32

f(12) = 128

Explanation:

Since we know the function that models the population we will replace all the elements that appear in the domain:

f(0)=8*(2)^(0/3) = 8*2^0 = 8*1 = 8

f(3)=8*(2)^(3/3) = 8*2^1 = 8*2= 16

f(6)=8*(2)^(6/3) = 8*(2)^2= 8*4 = 32

f(12)=8*(2)^(12/3) = 8*(2)^4 = 8*16 = 128

The corresponding results are shown in the graph that is attached.