For this case we have an equation of the form:
[tex] y = A * (b) ^ x
[/tex]
Where,
A: initial amount
b: growth rate
x: time in months
We must find the values of A and b.
For A we have:
[tex] 3 = A * (b) ^ 0
3 = A * 1
A = 3[/tex]
For B we have:
[tex] 32 = 3 * (b) ^ 4
[/tex]
Clearing b we have:
[tex]b = (32/3) ^ {(1/4)} b = 1.81[/tex]
Then, for 10 months we have:
[tex] y = 3 * (1.81) ^ {10} y = 1132[/tex]
Answer:
you will have in your barn 1132 mice after 10 months
