Mathematical Models: Linear Functions

Suppose your friend sells soda at the Tourist Games. Based on very careful record keeping he
has determined that for each degree the temperature increases, he sells eight more liters of soda
than he does when it is 62F. He sells 354 liters when it is 62F. The temperature varies
between 62F and 98F.

a. Construct a linear model to describe this situation mathematically.

b. Calculate the number of liters he sells when the temperature is

i) 65F
ii) 97F
i) 82F

c. How hot is it if he sells 442 liters?

d. What is the slope? (What other words would you use to describe this relation?

E. Sketch a graph of your function

2. For many years people have recognized a relationship between the temperature and the rate at
which crickets are chirping. The folk method of determining the temperature in degrees
Fahrenheit is to count the number of chirps in a minute and divide by 4, then add 40. In 1898, A.
E. Dolbear [3] noted that “crickets in a field synchronously, keeping time as if led by the wand of
a conductor.” In his paper, he appears to be the first person to write down a formula in a
scientific publication, giving a linear relationship for the temperature based on the chirp rate of
crickets.

a. Construct a linear model to describe this situation mathematically

b. Sketch a graph of your function

c. Calculate the chirp rate when the temperature is
ii) 84F

i) 65F

ii) 97F