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)=29,900(0.80)^t find the initial value of the car and the value after 11 years. round your answers to the nearest dollar as necessary. initial value: $ value after 11 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)=29,900(0.80)^t find the initial value of the car and the value after 11 years. round your answers to the nearest dollar as necessary. initial value: $ value after 11 years: $

Answer

Explanation:

Step1: Find initial value

Set (t = 0) in (v(t)=29900(0.80)^t). Since any non - zero number to the power of 0 is 1, (v(0)=29900(0.80)^0=29900\times1 = 29900).

Step2: Find value after 11 years

Set (t = 11) in (v(t)=29900(0.80)^t). Then (v(11)=29900\times(0.80)^{11}). Calculate ((0.80)^{11}\approx0.08589934592), and (v(11)=29900\times0.08589934592\approx2568).

Answer:

Initial value: $$29900$ Value after 11 years: $$2568$