Question

luna tracks her finances using a budgeting app. the app tells her that if she leaves the money in her savings account alone, the amount of money in the account after t years will be $400(1.06)^t$ dollars.
how does the money in the account change over time?
the amount of money increases by $400 every year.
the amount of money decreases by $400 every year.
the amount of money increases by 6% every year.
the amount of money decreases by 6% every year.

Explanation:

Step1: Recall compound growth formula

The general compound growth formula is $A = P(1 + r)^t$, where $P$ is principal, $r$ is annual growth rate, $t$ is time, and $A$ is final amount.

Step2: Match given formula to standard form

Given formula: $A = 400(1.06)^t$. Compare to $A = P(1 + r)^t$: $1 + r = 1.06$, so $r = 0.06 = 6\%$.

Step3: Determine growth direction

Since $r > 0$, the amount increases annually by this rate.

Answer:

The amount of money increases by 6% every year.