Question

question a researcher tracks a bacterial population in thousands of bacteria over time in hours. at time t = 8 hours, bacterial population is measured at 93.2 thousand bacteria. at time t = 11 hours, bacterial population is measured at 88.7 thousand bacteria. find the average rate of change from t = 8 to t = 11 hours, rounding your answer to three decimal places, with appropriate units. then fill in the guided sentence below to interpret the meaning of your answer in context. answer the average rate of change is. it represents that the is at a rate of over that time interval.

Explanation:

Step1: Identify the formula for average rate of change

The formula for the average rate of change of a function $y = f(t)$ from $t = a$ to $t = b$ is $\frac{f(b)-f(a)}{b - a}$. Here, $a = 8$, $f(a)=93.2$, $b = 11$, and $f(b)=88.7$.

Step2: Substitute values into the formula

$\frac{88.7 - 93.2}{11 - 8}=\frac{- 4.5}{3}$.

Step3: Calculate the result

$\frac{-4.5}{3}=-1.500$.

Answer:

The average rate of change is $- 1.500$ thousand bacteria per hour. It represents that the bacterial population is decreasing at a rate of $1.500$ thousand bacteria per hour over that time interval.