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# Rate of Change : Exponential Growth

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4.) Ever wonder why bacteria are so hard to contain ? A certain coloney of bacteria has an initinal population of 10,000. After t hours, the coloney has grown to a number P(t) given by P(t) = 10000(1+.86t + t^2).

a.) Find the growth rate (rate of change) of the population P with respect to time t. [FInd P'(t)]

b.) Find the number of bacteria present after 5 hours.

c.) Find the growth rate when t = 5

This means that at t = 5, there are ________ bacteria present, and the colony is growing at the rate of _______ per hour.

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Exponential growth and rates of change are investigated. The solution is detailed and well presented. The response received a rating of "5" from the student who originally posted the question.

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