Question

1. miguel tracked the weekly spread of two strains of flu virus. his data are shown below. compare the number of cases of flu by finding and interpreting average rates of change over the interval 0, 4. strain 1 week 0 1 2 3 4 5 cases 15 25 40 60 85 115 strain 2 which strain has the higher rate of change?

Explanation:

Step1: Recall average rate - of - change formula

The average rate of change of a function $y = f(x)$ over the interval $[a,b]$ is $\frac{f(b)-f(a)}{b - a}$.

Step2: Calculate average rate of change for Strain 1

For Strain 1, when $a = 0$, $f(0)=15$ and when $b = 4$, $f(4)=85$. Using the formula $\frac{f(4)-f(0)}{4 - 0}=\frac{85 - 15}{4}=\frac{70}{4}=17.5$ cases per week.

Step3: Estimate values for Strain 2 from the graph

From the graph of Strain 2, when $x = 0$, $y\approx15$ and when $x = 4$, $y\approx70$.

Step4: Calculate average rate of change for Strain 2

Using the average - rate - of - change formula, $\frac{y(4)-y(0)}{4 - 0}=\frac{70 - 15}{4}=\frac{55}{4}=13.75$ cases per week.

Answer:

Strain 1 has a higher rate of change.