the initial balance of a mutual fund is $1800. the fund is expected to grow in value at an annual rate of…

the initial balance of a mutual fund is $1800. the fund is expected to grow in value at an annual rate of 5%. let x represent the number of years since the fund was started. let y represent the value of the fund x years later. which equation models the value of the mutual fund x years after it was started? enter your answer in the box.

the initial balance of a mutual fund is $1800. the fund is expected to grow in value at an annual rate of 5%. let x represent the number of years since the fund was started. let y represent the value of the fund x years later. which equation models the value of the mutual fund x years after it was started? enter your answer in the box.

Answer

Explanation:

Step1: Recall compound - growth formula

The formula for compound - growth is $y = a(1 + r)^x$, where $a$ is the initial amount, $r$ is the growth rate as a decimal, and $x$ is the number of time periods.

Step2: Identify values of $a$ and $r$

Given that $a=$1800$ (initial balance) and $r = 5%=0.05$ (annual growth rate).

Step3: Substitute values into formula

Substitute $a = 1800$ and $r=0.05$ into $y = a(1 + r)^x$. We get $y=1800(1 + 0.05)^x=1800(1.05)^x$.

Answer:

$y = 1800(1.05)^x$