Find the growth rate after 3 hours.

Question

The population of a slowly growing bacterial colony after t hours is given by p(t) = 4t²+29t +200. Find the growth rate after 3 hours.

Answer 1

It might be easier to understand if you changed the question from "find the growth rate" to "find the population growth rate".

A rate means "take the derivative with respect to time". What equation? The population equation.

p(t) = 4t² + 29t + 200 so, using the power rule, the derivative is:

p'(t) = 8t + 29

Now, plug in t = 3:

p'(3) = 8(3) + 29

p'(3) = 53 bacteria/hr

Answer 2

Determine first derivative, p'(x)

Calculate p'(3)