Question Find the value of a piecewise function $w(t)$ when $t=-7$ .

Studdy Solution

STEP 1

Assumptions
1. The function $w(t)$ is defined piecewise with two different expressions.
2. The first expression $-3t + 8$ is valid for $t < -5$ .
3. The second expression $4t - 2$ is valid for $t \geq -5$ .
4. We are asked to find the value of $w(t)$ when $t = -7$ .

STEP 2

Determine which expression to use for $w(t)$ when $t = -7$ .
Since $-7 < -5$ , we use the first expression $-3t + 8$ .

STEP 3

Substitute $t = -7$ into the first expression to find $w(-7)$ .
$w(-7) = -3(-7) + 8$

STEP 4

Calculate the value of $w(-7)$ .
$w(-7) = -3(-7) + 8 = 21 + 8 = 29$
So, $w(-7) = 29$ .

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