Question Arielle starts with $500 in her bank account. Her balance increases by 3% each year. Find the exponential function f(x) to calculate her balance after x years.

Studdy Solution

STEP 1

1. Arielle's bank account balance increases by a fixed percentage of $3\%$ annually.
2. The increase in balance is compounded once per year.
3. The exponential function to describe the balance after $x$ years will be of the form $f(x) = P(1 + r)^x$ , where $P$ is the principal amount, $r$ is the annual interest rate (expressed as a decimal), and $x$ is the number of years.

STEP 2

1. Convert the annual increase percentage to a decimal.
2. Write the exponential function using the principal amount and the converted annual increase rate.
3. Simplify the function if necessary.

STEP 3

Convert the annual increase percentage of $3\%$ to a decimal.
$r = \frac{3}{100} = 0.03$

STEP 4

Write the exponential function using the principal amount of $\$500$ and the annual increase rate of $0.03$ .
$f(x) = 500(1 + 0.03)^x$

STEP 5

Simplify the function by combining the terms inside the parentheses.
$f(x) = 500(1.03)^x$
The exponential function to find the value of Arielle's bank account after $x$ years is:
$f(x) = 500(1.03)^x$

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