a vehicle depreciates according to the formula: $v = 20700(3.42)^{-0.06x}$ where $x$ is the age of the car…

a vehicle depreciates according to the formula: $v = 20700(3.42)^{-0.06x}$ where $x$ is the age of the car in years. find the value of the car when it is 14 years old. round to the nearest whole number. question help: post to forum

a vehicle depreciates according to the formula: $v = 20700(3.42)^{-0.06x}$ where $x$ is the age of the car in years. find the value of the car when it is 14 years old. round to the nearest whole number. question help: post to forum

Answer

Explanation:

Step1: Substitute the value of x

Substitute $x = 14$ into the formula $v=20700(3.42)^{- 0.06x}$. So we get $v = 20700\times(3.42)^{-0.06\times14}$.

Step2: Calculate the exponent

First, calculate $-0.06\times14=- 0.84$. Then the formula becomes $v = 20700\times(3.42)^{-0.84}$.

Step3: Calculate the power value

Calculate $(3.42)^{-0.84}=\frac{1}{(3.42)^{0.84}}$. Using a calculator, $(3.42)^{0.84}\approx2.677$, so $(3.42)^{-0.84}\approx\frac{1}{2.677}\approx0.374$.

Step4: Calculate the final value

Multiply $20700$ by $0.374$. $v=20700\times0.374 = 7741.8$.

Step5: Round the result

Round $7741.8$ to the nearest whole number, which is $7742$.

Answer:

$7742$