Question

the thomas family had an opportunity to by 50 acres of land for $800 per acre. in the past the price of land had risen 3% per year. how long will it be before the land is worth $1000 per acre? explained

Answer 1

Given:

Initial value = $800 per acre

Growth rate = 3% per year

To find:

How long will it be before the land is worth $1000 per acre.

Solution:

The exponential growth model is:

`y=a(1+r)^t`

Where, y is the new value, a is the initial value, r is the growth rate in decimal and t is the number of years.

Putting
`y=1000, a=800, r=0.03`, we get

`1000=800(1+0.03)^t`

`(1000)/(800)=(1.03)^t`

`1.25=(1.03)^t`

Taking log both sides, we get

`\log 1.25=\log (1.03)^t`

`0.09691=t\log (1.03)`

`0.09691=0.012837t`

Isolating the variable t, we get

`(0.09691)/(0.012837)=t`

`7.54927=t`

`t\approx 7.55`

Therefore, the land is worth $1000 per acre after 7.55 years.