Question

The number of dogs, D, housed at a county animal shelter is modeled by the function D  4 2M  50, where M is the number of months the shelter has been open. How many months will it take for 74 dogs to be housed at the shelter?

Answer 1

18 Months

Explanation:

The function which models the number of dogs, D, housed at a county animal shelter is:

`D=4√(2M) +50`

Where M=Number of months the shelter has been open.

Given the number of dogs, D = 74, we are required to determine the number of Months in which this will happen.

Using our given function:

`D=74\\D=4√(2M) +50\\74=4√(2M) +50\\74-50=4√(2M)\\24=4√(2M)`

Dividing both sides by 4

`6=√(2M)\\\text{Squaring both sides}\\6^2=(√(2M))^(2) \\2M=36\\\text{Dividing both sides by 2}\\M=18`

It will take 18 Months for 74 Dogs to be housed in the shelter.