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)=24,500(0.86)^t find the value of the car after 6 years and after 12 years. round your answers to the nearest dollar as necessary. value after 6 years: $ value after 12 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)=24,500(0.86)^t find the value of the car after 6 years and after 12 years. round your answers to the nearest dollar as necessary. value after 6 years: $ value after 12 years: $

Answer

Explanation:

Step1: Substitute t = 6

Substitute (t = 6) into (v(t)=24500(0.86)^{t}), we get (v(6)=24500\times(0.86)^{6}).

Step2: Calculate (v(6))

((0.86)^{6}=0.86\times0.86\times0.86\times0.86\times0.86\times0.86\approx0.405), then (v(6)=24500\times0.405 = 9922.5\approx9923).

Step3: Substitute t = 12

Substitute (t = 12) into (v(t)=24500(0.86)^{t}), we get (v(12)=24500\times(0.86)^{12}).

Step4: Calculate (v(12))

((0.86)^{12}=(0.86^{6})^{2}\approx0.405^{2}= 0.164), then (v(12)=24500\times0.164 = 4018).

Answer:

Value after 6 years: $$9923$ Value after 12 years: $$4018$