The population of a slowly growing bacterial colony after t hours is given by p(t)=3t2+29t+150 . Find the growth rate after 4 hours?

Answer 1

The growth rate is the derivative of the population, dp/dt.

dp/dt = 6t + 29

when t = 4, dp/dt = 24 + 29 = 53 bacteria per hour.

This exact method is based upon using differntial calculus. If you are unfamiliar with it, try calculating p at 4.05 and 3.95 h, taking the difference, and dividing by the time interval, 0.1 hours.
p(4.05) = 316.66
p(3.95) = 311.36
change during interval = 5.30
rate of change = 53

Answer 2

Like Drwls said above it's really a differential Calc question. Just take the differative of p(t)
p'(t) = 6t + 29 + 0 .
p'(4) = 6(4) + 29 = 53 bacteria/hr