Question

A family of 3 mice move into your barn. After 4 months, there are now 32 mice. At 10 months, how many mice will you have in your barn? (Show your work)

Answer 1

32-3 = 29 / 4 = 7.25 mice / month
29 + (10*7.25) = 29 + 72.5= 101.5
102 mice after 10 months

Answer 2

For this case we have an equation of the form:

`y = A * (b) ^ x`
Where,
A: initial amount
b: growth rate
x: time in months
We must find the values of A and b.
For A we have:

`3 = A * (b) ^ 0 3 = A * 1 A = 3`
For B we have:

`32 = 3 * (b) ^ 4`
Clearing b we have:

`b = (32/3) ^ {(1/4)}  b = 1.81`
Then, for 10 months we have:

`y = 3 * (1.81) ^ {10}   y = 1132`
Answer:
you will have in your barn 1132 mice after 10 months