11. the value of a car, in dollars, is depreciating according to the formula v = 37,000(3.21)^(-.05t) where…

11. the value of a car, in dollars, is depreciating according to the formula v = 37,000(3.21)^(-.05t) where t is the age of the car in years. find the value of the car when it is five and one - half years old to the nearest dollar.

11. the value of a car, in dollars, is depreciating according to the formula v = 37,000(3.21)^(-.05t) where t is the age of the car in years. find the value of the car when it is five and one - half years old to the nearest dollar.

Answer

Explanation:

Step1: Substitute the value of t

Given $t = 5.5$, substitute it into the formula $V = 37000(3.21)^{-0.05t}$. So we get $V=37000\times(3.21)^{-0.05\times5.5}$.

Step2: Calculate the exponent

First, calculate $-0.05\times5.5=- 0.275$. Then the formula becomes $V = 37000\times(3.21)^{-0.275}$.

Step3: Calculate the power - term

We know that $a^{-n}=\frac{1}{a^{n}}$, so $(3.21)^{-0.275}=\frac{1}{(3.21)^{0.275}}$. Using a calculator, $(3.21)^{0.275}\approx1.377$. Then $\frac{1}{(3.21)^{0.275}}\approx\frac{1}{1.377}\approx0.726$.

Step4: Calculate the value of V

Multiply 37000 by 0.726. $V = 37000\times0.726 = 26862$.

Answer:

26862