Answer:
18 Months
Step-by-step explanation:
The function which models the number of dogs, D, housed at a county animal shelter is:
[tex]D=4\sqrt{2M} +50[/tex]
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:
[tex]D=74\\D=4\sqrt{2M} +50\\74=4\sqrt{2M} +50\\74-50=4\sqrt{2M}\\24=4\sqrt{2M}[/tex]
Dividing both sides by 4
[tex]6=\sqrt{2M}\\\text{Squaring both sides}\\6^2=(\sqrt{2M})^{2} \\2M=36\\\text{Dividing both sides by 2}\\M=18[/tex]
It will take 18 Months for 74 Dogs to be housed in the shelter.
