Let's say that I was given the population formula:
P(t) = 2546e^(6t) where t is in years since 1986. How would I find the rate of change with this given formula?

Question

Let's say that I was given the population formula:
P(t) = 2546e^(6t) where t is in years since 1986. How would I find the rate of change with this given formula?

anonymous · Answer

The derivative which is 15276e^(6t) right? I was not given r in the problem.

freckles · Answer

oh okay I was doing growth rates or whatever it was called above

freckles · Answer

$$P(t)=ae^{bt} \ \implies P'(t)=a \cdot be^{bt}$$

freckles · Answer

yes 6*2546 is 15276

freckles · Answer

your derivative is right

freckles · Answer

did you want to find the rate of change at a certain number you just use the derivative there...

freckles · Answer

or if you wanted to find an average rate of change that is a little different

anonymous · Answer

Alright, thanks for the clarifications!

freckles · Answer

$$\text{ average rate of change from } x=a \text{ to } x=b \ \text{ would be } \frac{P(b)-P(a)}{b-a}$$