Question

The cost of a floral bouquet after a discount is applied is represented by the function below, where x represents the number of

Answer 1

The average rate of change over the interval $(12,24)$ is 2.17

Explanation:

Given that the cost of a floral bouquet after a discount is given by the function $f(x)=2.17x-10.00$

We need to determine the average rate of change over the interval $(12,24)$

The average rate of change can be determined using the formula,

$\frac{f(b)-f(a)}{b-a}$

where $a=12$ and $b=24$

Substituting the value of a and b in the function, we get,

$f(12)=2.17(12)-10.00$

        $=26.04-10.00$

        $=16.04$

$f(24)=2.17(24)-10.00$

        $=52.08-10.00$

        $=42.08$

Hence, substituting these values in the formula, we get,

$\frac{f(b)-f(a)}{b-a}=\frac{42.08-16.04}{24-12}$

Simplifying, we get,

$\frac{f(b)-f(a)}{b-a}=\frac{26.04}{12}$

Dividing, we have,

$\frac{f(b)-f(a)}{b-a}=2.17$

Thus, the average rate of change over the interval $(12,24)$ is 2.17