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

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

$\dfrac{1000}{800}=(1.03)^t$

$1.25=(1.03)^t$

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

$\dfrac{0.09691}{0.012837}=t$

$7.54927=t$

$t\approx 7.55$

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