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: [tex]y=a*b^x[/tex]; 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,
[tex]14\text{ percent}=\frac{14}{100}=0.14[/tex]
[tex]E(t)=590,000*(1+0.14)^t[/tex]
[tex]E(t)=590,000*(1.14)^t[/tex]
Now let us substitute the value for building in 2020 by substituting t=8 as 2020-2012=8.
[tex]E(2020)=590,000*(1.14)^8[/tex]
[tex]E(2020)=590,000*2.8525864220672256[/tex]
[tex]E(2020)=1,683,025.989019663104\approx 1,683,026[/tex]
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.
