Question

a homes value increases at an average rate of 5.5% each year. the current value is $120,000. what function can be used to find the value of the home after x years?
$f(x)=120,000(1.055x)$
$f(x)=120,000(0.055)^x$
$f(x)=(120,000)(1.055)^x$
$f(x)=120,000(1.055)^x$

Explanation:

Step1: Recall compound growth formula

The standard formula for exponential growth is $f(x) = P(1+r)^x$, where $P$ is the initial value, $r$ is the annual growth rate (in decimal), and $x$ is time in years.

Step2: Identify given values

Initial value $P = 120000$, growth rate $r = 5.5\% = 0.055$.

Step3: Substitute into formula

Substitute $P$ and $r$ into the growth formula:
$f(x) = 120000(1+0.055)^x = 120000(1.055)^x$

Step4: Eliminate incorrect options

• $f(x)=120,000(1.055x)$ is linear, not exponential growth.
• $f(x)=120,000(0.055)^x$ uses only the growth rate, not the total factor.
• $f(x)=[(120,000)(1.055)]^x$ incorrectly raises the initial value times growth factor to the power of $x$.

Answer:

$f(x) = 120,000(1.055)^x$