Question

A home has an original value of $249,000.each year,the value of the home decreases by 7.1 what equation models the solution after t years?

Answer 1

The value of home after t years is $249,000
`(0.929)^(\textrm t)`

Explanation:

Given as :

The original value of home = p = $249,000

The value of home depreciate every year at rate = r = 7.1%

Let The value of home after t years = A

Now, According to question

The value of home after t years = original value of home ×
`(1-(\textrm rate)/(100))^(\textrm time)`

Or, A = p ×
`(1-(\textrm r)/(100))^(\textrm t)`

Or, A = $249,000 ×
`(1-(\textrm 7.1)/(100))^(\textrm t)`

Or, A = $249,000 ×
`(0.929)^(\textrm t)`

So,The value of home after t years = A = $249,000
`(0.929)^(\textrm t)`

Hence,The value of home after t years is $249,000
`(0.929)^(\textrm t)` . Answer