Question

Suppose a population of 200 crickets doubles in size every month the function f(x) equals 200×2 to the X power gives the population after X months how many crickets will there be after three years

Answer 1

Answer: There will be 1.37 x 10^13 crickets after 3 years.

Explanation:

Hi, to answer this question we simply have to replace x in the formula by the number of months in 3 years.

f (x) = 200 (2^x)

Where x is the number of months

Since one year has 12 months,

for 3 years: 3 x 12 = 36 months

Substituting x= 36 on the function

f (36) = 200 (2^36)

f (36) = 200 (2^x)

f(36) = 1.37 x 10^13

Feel free to ask for more if needed or if you did not understand something.

Answer 2

≈ 1.37 *
`10^(13)`

Explanation:

Given the exponental function is:

F(x) = 200*
`2^(x)` where:

• 200 is initial value of crickets
• 2 is the base number (doubles in size every month)
• x is the number of months

How many crickets will there be after three years?

3 years = 12*3 = 36 so x = 36. Substitute x into the function we have:

F(x) = 200*
`2^(36)` ≈ 1.37 *
`10^(13)`

So the number of crickets after three years is: ≈ 1.37 *
`10^(13)`