Pregunta
D. \( f(x)=\left\{\begin{array}{ll}4.10+0.05747 x & \text { if } x \leq 1500 \\ 90.305+0.03788(x-1500) & \text { if } x>1500\end{array}\right. \) b) What is the monthly charge if 980 kWh are used? \( \$ \square \) (Type an integer or a decimal rounded to two decimal places as need
Ask by Wilson Reed. in the United States
Mar 15,2025
Solución de inteligencia artificial de Upstudy
Respuesta verificada por el tutor
Responder
The monthly charge for 980 kWh is \$60.42.
Solución
To find the monthly charge for 980 kWh, we need to determine which part of the function \( f(x) \) is applicable for \( x = 980 \) and then calculate the corresponding charge.
Given function:
\[ f(x) = \left\{\begin{array}{ll}4.10+0.05747x & \text{if } x \leq 1500 \\ 90.305+0.03788(x-1500) & \text{if } x > 1500\end{array}\right. \]
Since \( 980 \leq 1500 \), we use the first part of the function:
\[ f(x) = 4.10 + 0.05747x \]
Now, we substitute \( x = 980 \) into the function to find the monthly charge:
\[ f(980) = 4.10 + 0.05747 \times 980 \]
Let's calculate the monthly charge.
Calculate the value by following steps:
- step0: Calculate:
\(4.1+0.05747\times 980\)
- step1: Multiply the numbers:
\(4.1+56.3206\)
- step2: Add the numbers:
\(60.4206\)
The monthly charge for 980 kWh is $60.42.
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The Deep Dive
To find the monthly charge for using 980 kWh, we need to use the first part of the piecewise function since 980 is less than or equal to 1500. Using the formula \( f(x) = 4.10 + 0.05747 x \): \[ f(980) = 4.10 + 0.05747 \times 980 \] Calculating \( 0.05747 \times 980 \) gives: \[ 0.05747 \times 980 = 56.3306 \] Now plug that back into the equation: \[ f(980) = 4.10 + 56.3306 \approx 60.43 \] Therefore, the monthly charge for using 980 kWh is approximately \( \$60.43 \). So the final answer is: \( \$60.43 \)

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