The average rate of change over the interval [tex](12,24)[/tex] is 2.17
Explanation:
Given that the cost of a floral bouquet after a discount is given by the function [tex]f(x)=2.17x-10.00[/tex]
We need to determine the average rate of change over the interval [tex](12,24)[/tex]
The average rate of change can be determined using the formula,
[tex]\frac{f(b)-f(a)}{b-a}[/tex]
where [tex]a=12[/tex] and [tex]b=24[/tex]
Substituting the value of a and b in the function, we get,
[tex]f(12)=2.17(12)-10.00[/tex]
[tex]=26.04-10.00[/tex]
[tex]=16.04[/tex]
[tex]f(24)=2.17(24)-10.00[/tex]
[tex]=52.08-10.00[/tex]
[tex]=42.08[/tex]
Hence, substituting these values in the formula, we get,
[tex]\frac{f(b)-f(a)}{b-a}=\frac{42.08-16.04}{24-12}[/tex]
Simplifying, we get,
[tex]\frac{f(b)-f(a)}{b-a}=\frac{26.04}{12}[/tex]
Dividing, we have,
[tex]\frac{f(b)-f(a)}{b-a}=2.17[/tex]
Thus, the average rate of change over the interval [tex](12,24)[/tex] is 2.17
