Question

Here is a graph of P, an insect population, W weeks after it was first measured. The population grows Exponentially.

Please answer the following questions. (I WILL GIVE +POINTS)

Answer 1

Question 1

We can say that
`P=a \cdot b^w` for constants
`a` and
`b`.

Substituting the given points into this equation yields
`ab=900` and
`ab^3=8100`. We need to find the value of
`b` in this system.

`(ab^3)/(ab)=(8100)/(900) \implies b^2=9`

Since the graph shows exponential growth, take the positive square root. So,
`b=\boxed{3}`.

Question 2

We need to find the value of
`a`.

`ab=900 \implies 3a=900 \implies a=\boxed{300}`