question\na new car is purchased for 16600 dollars. the value of the car depreciates at 9.75% per…

question\na new car is purchased for 16600 dollars. the value of the car depreciates at 9.75% per year.\nwhat will the value of the car be, to the nearest cent, after 8 years?\nanswer attempt 1 out of 2\nsubmit answer

question\na new car is purchased for 16600 dollars. the value of the car depreciates at 9.75% per year.\nwhat will the value of the car be, to the nearest cent, after 8 years?\nanswer attempt 1 out of 2\nsubmit answer

Answer

Explanation:

Step1: Identificar la fórmula de depreciación

La fórmula para la depreciación exponencial es $V = P(1 - r)^t$, donde $P$ es el valor inicial, $r$ es la tasa de depreciación (en decimal) y $t$ es el tiempo en años. Aquí, $P = 16600$, $r = 0.0975$ (ya que $9.75% = \frac{9.75}{100} = 0.0975$) y $t = 8$.

Step2: Sustituir los valores en la fórmula

Sustituimos $P = 16600$, $r = 0.0975$ y $t = 8$ en la fórmula: $$V = 16600(1 - 0.0975)^8$$ Primero, calculamos $1 - 0.0975 = 0.9025$. Luego, calculamos $0.9025^8$.

Step3: Calcular $0.9025^8$

Usando una calculadora, $0.9025^8 \approx 0.47057$.

Step4: Calcular el valor final

Multiplicamos $16600$ por $0.47057$: $$V \approx 16600 \times 0.47057 \approx 7811.462$$

Step5: Redondear al centavo más cercano

Redondeamos $7811.462$ al centavo más cercano, que es $7811.46$.

Answer:

7811.46