Answer:
The population of moose after 12 years will be 7,692
Step-by-step explanation:
we know that
In this problem we have a exponential function of the form
[tex]y=a(b^x)[/tex]
where
y ----> population of moose
x ----> the time in years
a is the y-intercept or initial value
b is the base of the exponential function
we have
[tex]a=40[/tex] ----> the y-intercept is given in the table (value of y when the value of x is equal to zero)
substitute
[tex]y=40(b^x)[/tex]
Find the value of b
For x=1, y=62
substitute in the equation
[tex]62=40(b^1)\\b=62/40\\b=1.55[/tex]
therefore
[tex]y=40(1.55^x)[/tex]
What will be the population of moose after 12 years?
For x=12 years
substitute in the exponential equation
[tex]y=40(1.55^{12})[/tex]
[tex]y=7,692[/tex]
