A new automobile is purchased for $20,000. If V = 2,000 (0.8) x, gives the car's value after x years, about how long will it take for the car to be worth $820?

It will take 4 years

Step-by-step explanation:

Here, given the exponential equation that approximates the cost of a car after a certain amount of time, we are tasked with calculating the amount of time it will take to be worth a certain amount.

The exponential equation that approximates the cost of the car is given as;

V = 2,000 (0.8) ^x

Now, our V = 820 but we want to calculate x which gives the number of years. Substituting this value of V, we get;

820 = 2000 (0.8) ^x

divide through by 2000

0.41 = 0.8^x

Take the log of both sides

log 0.41 = log 0.8^x

log 0.41 = xlog 0.8

x = log 0.41/log 0.8

x = 3.99 which is approximately 4 years