Answer:
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
