question 1-5\nthe function $h(x) = 25,600(0.85)^x$ represents the approximate value, in dollars, of a truck…

question 1-5\nthe function $h(x) = 25,600(0.85)^x$ represents the approximate value, in dollars, of a truck $x$ years after the truck was purchased.\nwhich function best describes $h(m)$, the approximate value, in dollars, of the truck $m$ months after the truck was purchased?\n1 year=12 months\n$circ$ $h(m) = 25,600(0.0135)^m$\n$circ$ $h(m) = 25,600(0.0708)^m$\n$circ$ $h(m) = 25,600(0.8538)^m$\n$circ$ $h(m) = 25,600(0.9865)^m$

question 1-5\nthe function $h(x) = 25,600(0.85)^x$ represents the approximate value, in dollars, of a truck $x$ years after the truck was purchased.\nwhich function best describes $h(m)$, the approximate value, in dollars, of the truck $m$ months after the truck was purchased?\n1 year=12 months\n$circ$ $h(m) = 25,600(0.0135)^m$\n$circ$ $h(m) = 25,600(0.0708)^m$\n$circ$ $h(m) = 25,600(0.8538)^m$\n$circ$ $h(m) = 25,600(0.9865)^m$

Answer

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:

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