Question

the rent for an apartment was $6,600 per year in 2012. if the rent increased at a rate of 4% each year thereafter, use an exponential equation to find the rent for the apartment in 2017

Answer 1

the rent for the apartment in 2017 is $8,351.105

Step-by-step explanation

The initial rent was $6,600 per year in 2012.

The rate at which the rent increase is 4%

Exponential equation is given as

`f(x)=a(1+r)^{n\text{ x t}}`

Where a = intial amount

r = rate

t = time

n = period

Hence, the rent for apartment can be calculated as follows

`\begin{gathered} f(x)=a(1+r)^{n\text{ x t}} \\ r\text{ = 4\%} \\ r\text{ = }(4)/(100) \\ r\text{ = 0.04} \\ n\text{ = 6} \\ F(x)=6,600(1+0.04)^{6\text{ x 1}}_{} \\ f(x)=6,600(1.04)^6 \\ f(x)\text{ = 6,600(1.265)} \\ f(x)\text{ = \$8,351.105} \end{gathered}`

Therefore, the rent for the apartment in 2017 is $8,351.105