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Un plan de telétono celular cueyta 39 dolares datos lódices parales. Las is dolares por a gon by te por función del número de gos mensuate son ana mero de minotos usados, dadá cor. \[ C(x)=\left\{\begin{array}{ll} 39 & \text { s; } 0 \leq x \leq 2 \\ 39+15(x-2) & 5 ; x>2 \end{array}\right. \] Cncuentre \( C(0,5), C(2) \) y \( C(4) \)

Ask by Reyes Kelley. in Mexico
Mar 09,2025

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Tutor-Verified Answer

Answer

\( C(0.5) = 39 \), \( C(2) = 39 \), \( C(4) = 69 \)

Solution

**Paso 1. Identificar la función correspondiente según el valor de \( x \):** La función se define por tramos: - Para \( 0 \leq x \leq 2 \): \[ C(x) = 39 \] - Para \( x > 2 \): \[ C(x) = 39 + 15(x - 2) \] **Paso 2. Calcular \( C(0.5) \):** Como \( 0.5 \) está en el intervalo \( 0 \leq x \leq 2 \), se utiliza: \[ C(0.5) = 39 \] **Paso 3. Calcular \( C(2) \):** El valor \( 2 \) pertenece al primer tramo, por lo tanto: \[ C(2) = 39 \] **Paso 4. Calcular \( C(4) \):** Como \( 4 \) es mayor que \( 2 \), se usa el segundo tramo de la función: \[ C(4) = 39 + 15(4 - 2) \] Primero se calcula \( 4 - 2 \): \[ 4 - 2 = 2 \] Luego: \[ C(4) = 39 + 15 \times 2 = 39 + 30 = 69 \] **Resultado:** \[ C(0.5) = 39, \quad C(2) = 39, \quad C(4) = 69 \]

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Para encontrar los costos \( C(0.5), C(2) \) y \( C(4) \), simplemente sustituimos los valores en la función \( C(x) \). 1. Para \( C(0.5) \) (donde \( 0 \leq 0.5 \leq 2 \)): \[ C(0.5) = 39 \] 2. Para \( C(2) \) (donde \( 0 \leq 2 \leq 2 \)): \[ C(2) = 39 \] 3. Para \( C(4) \) (donde \( 4 > 2 \)): \[ C(4) = 39 + 15(4 - 2) = 39 + 15 \cdot 2 = 39 + 30 = 69 \] Por lo tanto, los costos son: - \( C(0.5) = 39 \) - \( C(2) = 39 \) - \( C(4) = 69 \)

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