Mathematics: 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

the thomas family had an opportunity to by 50

reddmeans6

18.06.2021

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.

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