Question

select the correct answer from each drop - down menu. the sawyer and ruiz families each bought a laptop computer at the same time. the resale values, in dollars, of the laptops are modeled by the given functions, where x is the number of years that each family has owned the laptop. sawyer family’s laptop: $f(x)=620(0.85)^{x}$ ruiz family’s laptop: |x|g(x)| |0|640| |2|480| |4|360| the family’s laptop has the greater initial resale value. during the first four years, the resale value of the sawyer family’s laptop decreases at an average rate the resale value of the ruiz family’s laptop.

Explanation:

Step1: Encontrar valor inicial Sawyer

La valor inicial se obtiene al evaluar $f(x)$ cuando $x=0$:
$f(0) = 620(0.85)^0 = 620 \times 1 = 620$

Step2: Comparar valores iniciales

El valor inicial del portátil de la familia Ruiz es $g(0)=640$. Al comparar: $640 > 620$

Step3: Calcular tasa promedio Sawyer

La tasa promedio de disminución en 4 años es $\frac{f(4)-f(0)}{4-0}$. Primero calculamos $f(4)$:
$f(4) = 620(0.85)^4 \approx 620 \times 0.5220 = 323.64$
Luego la tasa: $\frac{323.64 - 620}{4} = \frac{-296.36}{4} = -74.09$ (la negativa indica disminución)

Step4: Calcular tasa promedio Ruiz

La tasa promedio es $\frac{g(4)-g(0)}{4-0} = \frac{360 - 640}{4} = \frac{-280}{4} = -70$ (la negativa indica disminución)

Step5: Comparar tasas de disminución

Al comparar los valores absolutos: $74.09 > 70$, lo que significa que la disminución promedio de Sawyer es mayor.

Answer:

1. The Ruiz family's laptop has the greater initial resale value.
2. During the first four years, the resale value of the Sawyer family's laptop decreases at an average rate greater than the resale value of the Ruiz family's laptop.