Question

The value of Sara's new car decreases at a rate of 8% each year.

1.Write an exponential function to model the decrease in the car's value each month.
2.Write an exponential function to model the decrease in the car's value each week.
3.Write an exponential function to model the decrease in the car's value each day.
4.What relationship is there between the amount of decrease and the time interval measured?

Answer 1

1. V = Vo(1-r)^t.
Vo = Initial value of car.
r = 0.08/12mo. = 0.0067/mo.
t = Time in months.
V = Vo(1-0.0067)^1 = 0.9933Vo.

2. V = Vo(1-r)^t.
r = 0.08/52wks. = 0.00154/wk.
t = Time in weeks.
V = Vo(1-0.00154)^1 = 0.9985Vo.

3. V = Vo(1-r)^t.
r = 0.08/365da. = 0.000219/day.
V = Vo(1-0.000219)^1 = 0.9998Vo.










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