the dollar value v(t) of a certain car model that is t years old is given by the following exponential…

the dollar value v(t) of a certain car model that is t years old is given by the following exponential function. v(t)=25,900(0.78)^t find the initial value of the car and the value after 13 years. round your answers to the nearest dollar as necessary. initial value: $ value after 13 years: $

the dollar value v(t) of a certain car model that is t years old is given by the following exponential function. v(t)=25,900(0.78)^t find the initial value of the car and the value after 13 years. round your answers to the nearest dollar as necessary. initial value: $ value after 13 years: $

Answer

Explanation:

Step1: Encontrar el valor inicial

Para encontrar el valor inicial del coche, se sustituye (t = 0) en la función (v(t)=25900(0.78)^t). Como cualquier número elevado a la potencia 0 es 1 ((a^0 = 1) para (a\neq0)), entonces (v(0)=25900(0.78)^0=25900\times1 = 25900).

Step2: Encontrar el valor después de 13 años

Sustituir (t = 13) en la función (v(t)=25900(0.78)^t). Entonces (v(13)=25900\times(0.78)^{13}). Calculando ((0.78)^{13}\approx0.0397), y (v(13)=25900\times0.0397\approx1028).

Answer:

Initial value: $25900 Value after 13 years: $1028