Answer:
Step-by-step explanation:
The rate of change in any function is the slope of the line between 2 points. Our points are t = 2 and t = 5. But we know that the slope formula also involves the h's for each of those t's. We need to find them first. The slope formula is
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex], but for us it will look like this (fittted to our needs):
[tex]m=\frac{h_2-h_1}{t_2-t_1}[/tex]. So we need to find those h's.
when t = 2, plug in a 2 for t and solve for h.
Therefore, [tex]h(2)=-2(2)^2+8(2)+24[/tex] and
h(2) = 32 and in coordinate form, (2, 32).
When t = 5, plug in a 5 for t and solve for h.
Therefore, [tex]h(5) =-2(5)^2+8(5)+24[/tex] and
h(5) = 14 and in coordinate form, (5, 14). Now we can plug into our slope formula:
[tex]m=\frac{14-32}{5-2}=\frac{-18}{3}=-6[/tex] , choice B.
The rate of change is -6 which, in words, means that the ball fell 6 feet every 1 second it fell.
