18. A car depreciated (decreased in value) by 25% during the first year. If the car was purchased for $28,000, what is the car worth today?

Question

please explain how to solve this.

Answer 1

Rebecca, if you take 25% off the value, you have 75% of the previous value, right? This happens each year.

 

After one year, the car is worth 28,000(0.75) = 21,000.

 

After two years, it's worth 21,000(0.75) = 15,750. Starting from the original value of 28,000, that's 28,000(0.75)(0.75) = 15,750.

 

If you were to write a function with the value, v, as a function of t, the number of years...

 

v(t) = 28,000(0.75)^t

 

Conversly, if something appreciates in value, say by 5% every year with an original value of $400...

 

v(t) = 400(1.05)^t

 

Hope this helps!