Question

the exponential model below represents the balance of an investment, in dollars, $x$ years from now. what is meaning of 1.03 in the model?
$f(x)=6268(1.03)^x$
show your work here
hint: to add an exponent ($x^y$), type \exponent\ or press \^\
$\bigcirc$ every year, the investments balance decreases by 103%
$\bigcirc$ the investments balance will be zero after 3 years
$\bigcirc$ every year, the investments balance decreases by 3%
$\bigcirc$ every year, the investments balance increases by 103%
$\bigcirc$ every year, the investments balance increases by 3%
$\bigcirc$ the investment will have doubled in balance after 3 years

Explanation:

Step1: Recall exponential growth form

The standard exponential growth model is $f(x) = a(1+r)^x$, where $a$ is the initial amount, $r$ is the annual growth rate, and $x$ is time in years.

Step2: Match given model to standard form

The given model is $f(x) = 6268(1.03)^x$. Comparing to $a(1+r)^x$, we see $1+r = 1.03$.

Step3: Solve for growth rate $r$

Calculate $r = 1.03 - 1 = 0.03$, which is $3\%$. Since $1.03 > 1$, this represents growth.

Answer:

Every year, the investment's balance increases by 3%