Question

question 1-5
the function $h(x) = 25,600(0.85)^x$ represents the approximate value, in dollars, of a truck $x$ years after the truck was purchased.
which function best describes $h(m)$, the approximate value, in dollars, of the truck $m$ months after the truck was purchased?
1 year=12 months
$circ$ $h(m) = 25,600(0.0135)^m$
$circ$ $h(m) = 25,600(0.0708)^m$
$circ$ $h(m) = 25,600(0.8538)^m$
$circ$ $h(m) = 25,600(0.9865)^m$

Explanation:

Step1: Relate years to months

Since $x$ years equals $12x$ months, substitute $x=\frac{m}{12}$ into the original function.
$h(m)=25,600(0.85)^{\frac{m}{12}}$

Step2: Simplify the exponential term

Use exponent rule $a^{\frac{b}{c}}=(a^{\frac{1}{c}})^b$. Calculate $0.85^{\frac{1}{12}}$.
$0.85^{\frac{1}{12}} \approx 0.9865$

Step3: Rewrite the function

Substitute the simplified base back into the function.
$h(m)=25,600(0.9865)^m$

Answer:

$\boldsymbol{h(m) = 25, 600(0. 9865)^m}$