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$t$ $g(t)$ $-5$ $6$ $-4$ $4$ $-3$ $2$ $-2$ $1$ $g(t)$ $0$ $g(t)$ $0$ $g(t)$ $2$ $-2$ $1$ $-3$ $2$ $1$ $g(t)$ $8$ $g(t)$ $8$ $4$ $6$ $-5$ $2$ $-5$ $3$ What is the average rate of change of $-5$ $4$ over the interval $-5$ $5$ ? Give an exact number.

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Average rate of change II

Full solution

Q.

t

g(t)

-5

6

-4

4

-3

2

-2

1

g(t)

0

g(t)

0

g(t)

2

-2

1

-3

2

1

g(t)

8

g(t)

8

4

6

-5

2

-5

3

What is the average rate of change of

-5

4

over the interval

-5

5

? Give an exact number.

Find values at t: Find the values of $g(t)$ at $t = -4$ and $t = 1$ . $\newline$ $g(-4) = 4$ $\newline$ $g(1) = -3$
Calculate change in g(t): Calculate the change in $g(t)$ over the interval. $\newline$ Change in $g(t)$ = $g(1) - g(-4)$ $\newline$ Change in $g(t)$ = $-3 - 4$ $\newline$ Change in $g(t)$ = $-7$
Calculate change in t: Calculate the change in $t$ over the interval. $\newline$ Change in $t$ = $1 - (-4)$ $\newline$ Change in $t$ = $1 + 4$ $\newline$ Change in $t$ = $5$
Calculate average rate: Calculate the average rate of change. $\newline$ Average rate of change = $\frac{\text{Change in } g(t)}{\text{Change in } t}$ $\newline$ Average rate of change = $\frac{-7}{5}$ $\newline$ Average rate of change = $-1.4$

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