a new car is purchased for 20700 dollars. the value of the car depreciates at 11% per year. what will the…

Explanation:

Step1: Identify the depreciation formula

The formula for exponential - decay (depreciation) is $A = P(1 - r)^t$, where $P$ is the initial value, $r$ is the rate of depreciation as a decimal, and $t$ is the time in years.

Step2: Convert the rate to a decimal

The rate of depreciation $r = 11%=0.11$, the initial value $P = 20700$, and the time $t = 11$ years.

Step3: Substitute the values into the formula

$A=20700\times(1 - 0.11)^{11}=20700\times(0.89)^{11}$.

Step4: Calculate $(0.89)^{11}$

$(0.89)^{11}\approx0.29977$.

Step5: Calculate the value of the car

$A = 20700\times0.29977\approx6205.24$.

Answer:

$6205.24$