Question

the amount of cola in a soda machine decreases by a rate of 5% each hour. the amount of cola in the machine was originally 75 gallons. which function models the amount of cola in gallons after h hours? f(h) = -5(75)^h; f(h) = 75(.95)^h; f(h) =.95(75)^h; f(h) = 75(-5)^h

Explanation:

Step1: Identify decay formula

The general exponential decay function is $f(h) = a(1-r)^h$, where $a$ is the initial amount, $r$ is the decay rate, and $h$ is time.

Step2: Plug in given values

Initial amount $a=75$, decay rate $r=0.05$, so $1-r=0.95$. Substitute into the formula:
$f(h) = 75(0.95)^h$

Step3: Match to options

Compare the derived function to the provided choices.

Answer:

f(h) = 75(.95)^h