Question

Real estate values in a town are increasing at a rate of 14% per year.

Answer 1

Answer:

$1,093,026

Step-by-step explanation:

We have been given that real estate values in a town are increasing at a rate of 14% per year.  Mrs. Knoxville purchased a building for $590,000 in 2012.

We are told that real estate values are increasing at a rate of 14%, this means that values of real estates are increasing exponentially.

Since we know that an exponential function is in form: $y=a*b^x$; for growth b=(1+r), where r= growth rate in decimal form.

a= Initial value.

Let E(t) be value of real estates t years after 2012. Now let us substitute our given values in exponential function form.

Upon converting our increase rate to decimal form we will get,

$14\text{ percent}=\frac{14}{100}=0.14$

$E(t)=590,000*(1+0.14)^t$

$E(t)=590,000*(1.14)^t$

Now let us substitute the value for building in 2020 by substituting t=8 as 2020-2012=8.

$E(2020)=590,000*(1.14)^8$

$E(2020)=590,000*2.8525864220672256$

$E(2020)=1,683,025.989019663104\approx 1,683,026$

Now let us subtract 590,000 from 1683026 to find the amount that Mrs. Knoxville can get from selling the building.

1,683,026-590,000=1,093,026

Therefore, Mrs. Knoxville can get $1,093,026 from selling the building.