Question

Amber bought a condominium at a time when prices were at their highs. She paid $200,000. Since then, the market value has decrease by 5% per year. Write an exponential depreciation equation to model this situation. Approximately when will Amber's condominium be worth less than $140,000?

Answer 1

$140,000(1 - .05)^t

Explanation:

you have your total amount $140,000

it is decreased by 5% go behind the number and move two decimal points and you get .05

since is decreasing it would be 1 subtracted by ,05

$140,000(1 - .05)^t

"t" is the years it would be depreciated by

I do not see years but by knowledge i would say it is decreasing

Answer 2

Since, the exponential decay function,

`A=P(1-r)^t`

Where,

P = initial value,

r = rate per period,

t = number of periods,

Here, P = $ 200,000, r = 5% = 0.05,

Thus, the value of the condominium would be,

`A=200000(1-0.05)^t=200000(0.95)^t`

Which is the required equation.

If A < 140,000

`200000(0.95)^t < 140000`

By the graphing calculator.

`t< 6.95364`

Hence, about after 7 years the condominium will be worth less than $140,000.