Question

the exponential model below represents the balance of an investment, in dollars, $x$ years from now. what is meaning of 1.04 in the model?
$f(x)=19205(1.04)^x$
show your work here
hint: to add an exponent ($x^y$), type \exponent\ or press \^\
$\bigcirc$ every year, the investments balance decreases by 104%
$\bigcirc$ every year, the investments balance decreases by 4%
$\bigcirc$ the investment will have doubled in balance after 4 years
$\bigcirc$ every year, the investments balance increases by 4%
$\bigcirc$ the investments balance will be zero after 4 years
$\bigcirc$ every year, the investments balance increases by 104%

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

Given $f(x)=19205(1.04)^x$, compare to $a(1+r)^x$. Here, $1+r=1.04$.

Step3: Solve for growth rate $r$

Calculate $r = 1.04 - 1 = 0.04$, which is $4\%$.

Step4: Interpret the value 1.04

Since $1+r=1.04$, this means the investment is multiplied by 1.04 each year, equivalent to a 4% annual increase.

Answer:

Every year, the investment's balance increases by 4%