Math / Algebra

Questioncompute the monthly cost for a subscriber, where $x$ is the number of $C(x)=\left\{\begin{array}{ll} 19.99 & \text { if } 0<x \leq 250 \\ 0.25 x-42.51 & \text { if } x>250 \end{array}\right.$
Compute the monthly cost of the cellular phone for use of the followi (a) 150 (b) 300 (c) 251 (a) $C(150)=\$ \square$ (Round to the nearest cent as needed.)

Studdy Solution

STEP 1

1. The cost function $C(x)$ for the cellular phone usage is piecewise defined.
2. For $0 < x \leq 250$ , the cost is a flat rate of \$19.99.
3. For $x > 250$, the cost is calculated using the linear function $0.25x - 42.51$.
4. We need to evaluate the cost for specific values of $x$ and round to the nearest cent if necessary.

STEP 2

1. Evaluate $C(x)$ for $x = 150$ using the appropriate piece of the piecewise function.
2. Evaluate $C(x)$ for $x = 300$ using the appropriate piece of the piecewise function.
3. Evaluate $C(x)$ for $x = 251$ using the appropriate piece of the piecewise function.

STEP 3

Determine which piece of the piecewise function applies for $x = 150$ .
Since $0 < 150 \leq 250$ , we use the first piece of the function: $C(x) = 19.99$ .

STEP 4

Compute $C(150)$ .
$C(150) = 19.99$

STEP 5

Determine which piece of the piecewise function applies for $x = 300$ .
Since $300 > 250$ , we use the second piece of the function: $C(x) = 0.25x - 42.51$ .

STEP 6

Compute $C(300)$ .
$C(300) = 0.25 \times 300 - 42.51$ $C(300) = 75 - 42.51$ $C(300) = 32.49$

STEP 7

Determine which piece of the piecewise function applies for $x = 251$ .
Since $251 > 250$ , we use the second piece of the function: $C(x) = 0.25x - 42.51$ .

STEP 8

Compute $C(251)$ .
$C(251) = 0.25 \times 251 - 42.51$ $C(251) = 62.75 - 42.51$ $C(251) = 20.24$
The monthly costs are as follows: (a) $C(150) = \$19.99$ (b) $C(300) = \$32.49$ (c) $C(251) = \$20.24$

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Studdy Solution

STEP 1

STEP 2

1. Evaluate $C(x)$ for $x = 150$ using the appropriate piece of the piecewise function.
2. Evaluate $C(x)$ for $x = 300$ using the appropriate piece of the piecewise function.
3. Evaluate $C(x)$ for $x = 251$ using the appropriate piece of the piecewise function.

STEP 3

Determine which piece of the piecewise function applies for $x = 150$ .
Since $0 < 150 \leq 250$ , we use the first piece of the function: $C(x) = 19.99$ .

STEP 4

Compute $C(150)$ .
$C(150) = 19.99$

STEP 5

Determine which piece of the piecewise function applies for $x = 300$ .
Since $300 > 250$ , we use the second piece of the function: $C(x) = 0.25x - 42.51$ .

STEP 6

Compute $C(300)$ .
$C(300) = 0.25 \times 300 - 42.51$ $C(300) = 75 - 42.51$ $C(300) = 32.49$

STEP 7

Determine which piece of the piecewise function applies for $x = 251$ .
Since $251 > 250$ , we use the second piece of the function: $C(x) = 0.25x - 42.51$ .

STEP 8

Compute $C(251)$ .
$C(251) = 0.25 \times 251 - 42.51$ $C(251) = 62.75 - 42.51$ $C(251) = 20.24$
The monthly costs are as follows: (a) $C(150) = \$19.99$ (b) $C(300) = \$32.49$ (c) $C(251) = \$20.24$

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Studdy Solution

STEP 1

STEP 2

STEP 3

Determine which piece of the piecewise function applies for x=150x = 150x=150.Since 0<150≤2500 < 150 \leq 2500<150≤250, we use the first piece of the function: C(x)=19.99C(x) = 19.99C(x)=19.99.

STEP 4

Compute C(150)C(150)C(150).C(150)=19.99 C(150) = 19.99 C(150)=19.99

STEP 5

Determine which piece of the piecewise function applies for x=300x = 300x=300.Since 300>250300 > 250300>250, we use the second piece of the function: C(x)=0.25x−42.51C(x) = 0.25x - 42.51C(x)=0.25x−42.51.

STEP 6

Compute C(300)C(300)C(300).C(300)=0.25×300−42.51 C(300) = 0.25 \times 300 - 42.51 C(300)=0.25×300−42.51 C(300)=75−42.51 C(300) = 75 - 42.51 C(300)=75−42.51 C(300)=32.49 C(300) = 32.49 C(300)=32.49

STEP 7

Determine which piece of the piecewise function applies for x=251x = 251x=251.Since 251>250251 > 250251>250, we use the second piece of the function: C(x)=0.25x−42.51C(x) = 0.25x - 42.51C(x)=0.25x−42.51.

STEP 8

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Determine which piece of the piecewise function applies for $x = 150$ .
Since $0 < 150 \leq 250$ , we use the first piece of the function: $C(x) = 19.99$ .

Compute $C(150)$ .
$C(150) = 19.99$

Determine which piece of the piecewise function applies for $x = 300$ .
Since $300 > 250$ , we use the second piece of the function: $C(x) = 0.25x - 42.51$ .

Compute $C(300)$ .
$C(300) = 0.25 \times 300 - 42.51$ $C(300) = 75 - 42.51$ $C(300) = 32.49$

Determine which piece of the piecewise function applies for $x = 251$ .
Since $251 > 250$ , we use the second piece of the function: $C(x) = 0.25x - 42.51$ .