Answer
a) $f(t)=10t+300$.
b) $100$ minutes
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 the pond filling: $a=10~gal/min$
The y−intercept is the initial amount of water: $300gal$. Thus: $f(t)=300$ at $t=0$, and $b=300$.
Hence, the linear model is:
$f(t)=10t+300$.
b) Plugging in $f(t)=1300$, we get:
$1300=10t+300\\1000=10t\\100=t$
Thus it takes $100$ minutes to fill the pond.
