A strain of bactena is placed into a nutnent broth at 30 deg

A strain of bactena is placed into a nutnent broth at 30 degrees C and allowed to grow The data shown to the right are collected. The population is measured in grams and the time in hours Since population P depends on time t and each input corresponds to exactly one output, we say that population is a function of time; so P(t) represents the population at time t. Find the average rate of change of the population from 0 to 3.5 hours On average, the population is Increasing at a rate of gram per hour from 0 to 3.5 hours.

Solution

average rate of change from a to b = [f(b)-f(a)]/(b-a)

a)from 0 to 3.5

average rate of change =[0.12-0.03]/(3.5-0)

average rate of change = 0.09/3.5

average rate of change =0.026

on average, the population is increasing at rate of 0.026 gm per hour from 0 to 3.5 hours