Question

G(t)=−(t−1)2+5g, left parenthesis, t, right parenthesis, equals, minus, left parenthesis, t, minus, 1, right parenthesis, squared, plus, 5 What is the average rate of change of gggg over the interval −4≤t≤5-4\leq t\leq 5−4≤t≤5minus, 4, is less than or equal to, t, is less than or equal to, 5?

Answer 1

The average rate of change over is 1

Explanation:

Given that the function is $G(t)=-(t-1)^2+5$

We need to determine the average rate of change over the interval $-4\leq t\leq 5$

The value of G(-4):

The value of G(-4) can be determined by substituting t = -4 in the function $G(t)=-(t-1)^2+5$

Thus, we have,

$G(-4)=-(-4-1)^2+5$

$G(-4)=-(-5)^2+5$

$G(-4)=-(25)+5$

$G(-4)=-20$

Thus, the value of G(-4) = -20

The value of G(5):

The value of G(5) can be determined by substituting t = 5 in the function $G(t)=-(t-1)^2+5$, we get,

$G(5)=-(5-1)^2+5$

$G(5)=-(4)^2+5$

$G(5)=-16+5$

$G(5)=-11$

Thus, the value of G(5) is -11

Average rate of change:

The average rate of change can be determined using the formula,

$\frac{G(b)-G(a)}{b-a}$

where $a=-4$ and $b=5$

Substituting the values, we get,

$\frac{G(5)-G(-4)}{5-(-4)}$

Substituting $G(5)=-11$ and $G(-4)=-20$, we get,

$\frac{-11+20}{5+4}$

$\frac{9}{9}=1$

Thus, the average rate of change over the interval $-4\leq t\leq 5$ is 1.