Question

On June 1, a fast-growing species of algae is accidentally introduced into a lake in a city park. It starts to grow and

cover the surface of the lake in such a way that the area it covers doubles every day. If it continues to grow
unabated, the lake will be totally covered, and the fish in the lake will suffocate. At the rate it is growing, this will
happen on June 30.
d. Write an explicit formula for the sequence that models the percentage of the surface area of the lake that is
covered in algae, aa, given the time in days, tt, that has passed since the algae was introduced into the lake.

Answer 1

`A(t) = aa*2^t`

Explanation:

The area that is covered by the the algae doubles each day, so the first day it wil be aa, passing one day it will be 2xaa, two days 2x2xaa, and then successively, so for tt days:

`A(t) = aa*2^t`