Answer:
[tex]Rate = 19[/tex]
Step-by-step explanation:
Given
[tex]y = x^2 + 3x[/tex]
[tex]1 \le x \le 15[/tex]
Required
Determine the average rate of change
This is calculated as:
[tex]Rate = \frac{f(b) - f(a)}{b - a}[/tex]
Where
a = 1 and b = 15
So, we have:
[tex]Rate = \frac{f(15) - f(1)}{15 - 1}[/tex]
[tex]Rate = \frac{f(15) - f(1)}{14}[/tex]
Solve f(15):
[tex]f(15) = 15^2 + 3*15 = 270[/tex]
Solve f(1)
[tex]f(1) = 1^2 + 3*1 = 4[/tex]
So:
[tex]Rate = \frac{f(15) - f(1)}{14}[/tex]
[tex]Rate = \frac{270- 4}{14}[/tex]
[tex]Rate = \frac{266}{14}[/tex]
[tex]Rate = 19[/tex]
