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A strain of E.coli Beu 397-recA441 is placed into a nutrient broth at 3030^{\circ} Celsius and allowed to grow. The data shown in the table 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 can say that population is a function of time; so P(t) represents the population at time t.

Time (hours), tPopulation (grams), P00.\begin{matrix} \text{Time (hours), t} & \text{Population (grams), P}\\ \text{0} & \text{0.09}\\ \text{2.5} & \text{0.18}\\ \text{3.5} & \text{0.26}\\ \text{4.5} & \text{0.35}\\ \text{6} & \text{0.50}\\ \end{matrix}

Find the average rate of change of the population from 4.5 to 6 hours.


Step 1
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Note that the average rate of change is same as the slope of the line joining two points.

Average rate of change=ΔyΔx=0.50.3564.5=0.151.5=0.1 grams/hour\text{Average rate of change}=\dfrac{\Delta y}{\Delta x} = \dfrac{0.5-0.35}{6-4.5} = \dfrac{0.15}{1.5} = 0.1\text{ grams/hour}

This means that the population increased at an average rate of 0.1 grams/hour.

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