Invasive species often experience exponential population growth (ini- tially) wh

Question

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?

Explanation / Answer

we have to use the following formula

y(t)=y0ekt

17 = 5 ek * 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

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