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Population growth: There are originally 255 foxes and 104 rabbits on a particular game reserve. The fox population grows at a rate of 33 foxes per year, and the rabbits increase at a rate of 53 rabbits per year. Under these conditions, how long does it take for the number of rabbits to catch up with the number of foxes? How many of each animal will be present at that time?

Fahrenheit and Celsius: If you know the temperature \(C\) in degrees Celsius, you can find the temperature \(F\) in degrees Fahrenheit from the formula $$ F=\frac{9}{5} C+32 . $$ At what temperature will a Fahrenheit thermometer read exactly twice as much as a Celsius thermometer?

Expansion of steam: When water changes to steam, its volume increases rapidly. At a normal atmospheric pressure of \(14.7\) pounds per square inch, water boils at 212 degrees Fahrenheit and expands in volume by a factor of 1700 to 1 . But when water is sprayed into hotter areas, the expansion ratio is much greater. This principle can be applied to good effect in fire fighting. The steam can occupy such a large volume that oxygen is expelled from the area and the fire may be smothered. The table below shows the approximate volume, in cubic feet, of 50 gallons of water converted to steam at the given temperatures, in degrees Fahrenheit. $$ \begin{array}{|c|c|} \hline T=\text { Temperature } & V=\text { cubic } \\ \text { feet of steam } \\ \hline 212 & 10,000 \\ \hline 400 & 12,500 \\ \hline 500 & 14,100 \\ \hline 800 & 17,500 \\ \hline 1000 & 20,000 \\ \hline \end{array} $$ a. Make a linear model of volume \(V\) as a function of \(T\). b. If one fire is 100 degrees hotter than another, what is the increase in the volume of steam produced by 50 gallons of water? c. Calculate \(V(420)\) and explain in practical terms what your answer means. d. At a certain fire, 50 gallons of water expanded to 14,200 cubic feet of steam. What was the temperature of the fire?