Question

7. The rent for an apartment was $5,600 per year in 2018. If the

rent increased at a rate of 4% each year thereafter, use an
exponential equation to find the rent of the apartment in 2025.

Answer 1

9514 1404 393

Answer:

$7369

Explanation:

An exponential function is of the form ...

f(x) = a·b^x

where 'a' is the initial value, and 'b' is the growth factor. When the growth is given as a growth rate (4% per year), the growth factor is that value plus 1.

Here, the initial value, for x=0 in 2018, is 5600. So, the exponential model of the rent is ...

r(x) = 5600·(1 +.04)^x

r(x) = 5600·1.04^x . . . . . . . for x years after 2018

__

In 2025, we have x=2025 -2018 = 7. Then the rent is ...

r(7) = 5600·1.04^7 ≈ 7369

The rent of the apartment in 2025 is $7369 per year.