Questions: Today's school lunch was inappropriately thrown over the school fence by Mr. Kelly. For 0 ≤ t ≤ 90, the amount of food remaining (assuming no animals eat it) is modeled by F(t)=544.311(0.907)^t, where F(t) is measured in grams and t is measured in days. Find the average rate of change of F(t) over the interval 0 ≤ t ≤ 90. Indicate units of measure.

Today's school lunch was inappropriately thrown over the school fence by Mr. Kelly. For 0 ≤ t ≤ 90, the amount of food remaining (assuming no animals eat it) is modeled by F(t)=544.311(0.907)^t, where F(t) is measured in grams and t is measured in days. Find the average rate of change of F(t) over the interval 0 ≤ t ≤ 90. Indicate units of measure.

Transcript text: Today's school lunch was inappropriately thrown over the school fence by Mr. Kelly. For $0 \leq t \leq 90$, the amount of food remaining (assuming no animals eat it) is modeled by $F(t)=544.311(0.907)^{t}$, where $F(t)$ is measured in grams and $t$ is measured in days. Find the average rate of change of $F(t)$ over the interval $0 \leq$ $t \leq 90$. Indicate units of measure.

Solution

Solution Steps

To find the average rate of change of the function $ F(t) $ over the interval $ 0 \leq t \leq 90 $, we need to calculate the difference in the function values at the endpoints of the interval and divide by the length of the interval. This is done using the formula for the average rate of change: $\frac{F(b) - F(a)}{b - a}$, where $ a = 0 $ and $ b = 90 $.

Step 1: Define the Function and Interval

The function modeling the amount of food remaining is given by $ F(t) = 544.311 \times (0.907)^t $. We are tasked with finding the average rate of change of $ F(t) $ over the interval $ 0 \leq t \leq 90 $.

Step 2: Calculate Function Values at Interval Endpoints

Calculate $ F(0) $ and $ F(90) $: