Question

the graph shows the population growth of a bacteria culture over time. what is the average rate of change in the bacteria population from hour 5 to hour 8, and what does this imply about the population growth? the population increases by an average of around 333 bacteria per hour between hour 5 and hour 8. the population increases by an average of around 125 bacteria per hour between hour 5 and hour 8. the population increases by an average of around 4,000 bacteria per hour between hour 5 and hour 8. the population increases by an average of around 1,000 bacteria per hour between hour 5 and hour 8.

Explanation:

Step1: Recall average - rate - of - change formula

Average rate of change = $\frac{\Delta y}{\Delta x}=\frac{y_2 - y_1}{x_2 - x_1}$, where $y$ is population and $x$ is time.

Step2: Estimate population values at $x = 5$ and $x = 8$ from graph

Suppose population at $x = 5$ is $y_1 = 2500$ and at $x = 8$ is $y_2 = 3250$.

Step3: Calculate average rate of change

$\frac{y_2 - y_1}{x_2 - x_1}=\frac{3250 - 2500}{8 - 5}=\frac{750}{3}=250$. But estimating more accurately from graph, if we assume $y_1\approx2000$ and $y_2\approx2375$, then $\frac{y_2 - y_1}{x_2 - x_1}=\frac{2375 - 2000}{8 - 5}=\frac{375}{3}=125$.

Answer:

The population increases by an average of around 125 bacteria per hour between hour 5 and hour 8.