Invasive species often experience exponential population gro

Invasive species often experience exponential population growth (ini- tially) when introduced into a new environment. Zebra mussels are an invasive species that have recently made their way into midwestern lakes. Five zebra mussels were placed in a local lake, and in six months, there were 17 zebra mussels. Find the exponential model for the zebra mussel population. How many zebra mussels will be in the lake after 32 months? How many months will pass before the lake has one million zebra mussels?

Solution

we have to use the following formula

y(t)=y₀e^kt

17 = 5 e^{k * 6}

taking ln on both sides

ln(17/5) = 6k

k=ln(17/5)/6

k=0.204

y(t)= 5e^.204t

y(32) = 5 e^.204*32 = 3420