Isaac purchased a house for $169,200.00. Every year, Isaac makes improvements so that the value of the house goes up by 3%. Which of the following inequalities can be used to determine the number of years after purchase, $ f $, that the value of Isaac's house will be more than $186,120.00?

A. [tex]169,200.00(1+0.03)^t > 186,120.00[/tex]
B. [tex]186,120.00(0.03)^1 > 186,120.00[/tex]
C. [tex]169,200.00(1+0.03)^{t+1} > 186,120.00[/tex]
D. [tex]169,200.00(1-0.03)^t > 186,120.00[/tex]

The inequality that can be used to determine the number of years after purchase, f, that the value of Isaac's house will be more than $186,120.00 is $186,120.00(1+0.03)^t>$186,966.00 (option A).

Explanation:

The inequality that can be used to determine the number of years after purchase, f, that the value of Isaac's house will be more than $186,120.00 is:

$186,120.00(1+0.03)t>$186,966.00

The initial value of the house is $169,200.00.
The value of the house increases by 3% every year.
We can represent the value of the house after t years as $169,200.00(1+0.03)t.
To determine the number of years after purchase, f, that the value of Isaac's house will be more than $186,120.00, we need to solve the inequality:

$169,200.00(1+0.03)t>$186,120.00

Therefore, the correct inequality is $186,120.00(1+0.03)t>$186,966.00 (option A).