Devon purchased a new car valued at $16,000 that depreciated continuously at a rate of 35%. its current value is $2,000. the equation 2000=16000(1-r)^2 represents the situation, where t is the age of the car in years and r is the rate of depreciation. about how old is devon’s car? use a calculator and round your answer to the nearest whole number. 1 year 2 year 5 year 8 year

I hope the equation will be 2000=16000(1-r)^t because t is missing in the equation which we need to find.

Given rate: r= 35%= 0.35.

So, first step is to plug in 0.35 for r in the given formula to get the value of t.

Hence, the equation will be:

2000=16000(1-0.35)^t

2000=16000(0.65)^t (By subtraction)

2000/16000= 16000(0.65)^t /16000 (Dividing each sides by 16000)

0.125 = 0.65^t (By simplifying).

log 0.125 = log 0.65^t (Taking log each sides to isolate t).

log 0.125 = t log 0.65 (By applying the log property).

(Dividing each sides by log 0.65)

-0.903/-0.187 =t

t= 4.83

t= 5 ( Rounded to nearest integers)

So, Devon's car is 5 years old.

answer: 414,377,008

step-by-step explanation:

just multiply it