MATH SOLVE

4 months ago

Q:
# If x represents time, the average rate of change of the function f(x) in the first three seconds is ___.

Accepted Solution

A:

AnswerIf x represents time, the average rate of change of the function f(x) in the first three seconds is -50.ExplanationThe average rate of change of a linear function is the slope of the liner function. To find the slope of our linear function, we are using the slope formula: [tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]where[tex]m[/tex] is the slope of the line[tex](x_{1},y_{1})[/tex] are the coordinates of the first point on the line[tex](x_{2},y_{2})[/tex] are the coordinates of the second pointFrom our graph we can get the points (0, 150) and (3, 0), so [tex]x_{1}=0[/tex], [tex]y_{1}=150[/tex], [tex]x_{2}=3[/tex], and [tex]y_{2}=0[/tex]. Let's replace the values in our formula to find the slope of our linear function:[tex]m=\frac{0-150}{3-0}[/tex][tex]m=\frac{-150}{3}[/tex][tex]m=-50[/tex]Since the average of change a linear function is equal to its slope, the average rate of change of the function in the first three seconds is -50