Answer
a) $f(t)=0.5t+2$
b) $26$ seconds
Work Step by Step
We wish to obtain a linear model of the form $y=at+b$.
a) The rate of change is the rate of hydrogen filling: $a=0.5~ft^3/s$
The $y-intercept$ is the initial amount of hydrogen $2~ft^3$. Thus: $f(t)=2$ at $t=0$, and $b=2$.
Hence, the linear model is:
$f(t)=0.5t+2$.
b) Plugging in $f(t)=15$, we get:
$15=0.5t+2\\13=0.5t\\26=t$
Thus, it takes $26$ seconds to fill the balloon.
