The length of time that milk (and many other perishable substances) will stay fresh depends on the storage temperature. Suppose that milk will stay fresh for 146 hours in a refrigerator at 4°C. Milk that is left out in the kitchen at 22°C will keep for only 42 hours. Because bacteria grow exponentially, you can assume that freshness decays exponentially.
a. Write an equation that expresses the number of hours, h, that milk will keep in terms of the temperature, T.
b. Use your equation to predict how long milk will keep at 30°C and at 16°C.
c. If a container of milk soured after 147 hours, what was the temperature at which
it was stored?
d. Graph the relationship between hours and temperature, using your equation from 4a and the five data points you have found.
e. What is a realistic domain for this relationship? Why?