Question

Suppose in January, 𝑡=1 , a lake is covered by 2 square meters of algae. Every month, the area covered by algae doubles. (Assume that the growth occurs continuously.) Find the growth rate as a function of time with units square meters per month. Enter t for 𝑡 in months.

Answer 1

I shall assume that the area is 2 m^2 on January 1.
Then at the end of month t, the area will be
a = 2*2^t = 2^(t+1)
I guess if you want the growth rate, that would be
da/dt = ln2 * 2^(t+1) m^2/mo

Answer 2

da/dt=2^t*ln(2)