Question

The temperature, t, in degrees Fahrenheit, can be found by counting the number of cricket chirps, c, heard in 14 seconds and then adding 40. The equation t = c + 40 models the relationship between the temperature and the number of cricket chirps. What is true about the graph that represents this real-world scenario? Check all that apply.

Answer 1

Cricket Problem: Based on information in Deep River Jim's Wilderness Trailbook, the rate at which crickets chirp is a lenear function of temperature. At 55 degrees F they make 70 chirps per minute and at 69 degrees F they make 126 chirps per minute.

Answer 2

The graph is continuous.

A viable solution is (10, 50).

Explanation:

The given equation is

`t=c+40`

This equation models the relationship between the temperatura and the number of cricket chirps.

Where
`t` is temperature in degress Fahrenheit and
`c` is the number of cricket chirps heard in 14 seconds.

According to the problem, the temperature can be found by counting the number of cricket chirps heard in 14 seconds and then adding 40.

Now, the choices to this question are

The graph is continuous.

All values of t must be positive.

A viable solution is (–2, 38).

A viable solution is (0.5, 40.5).

A viable solution is (10, 50).

The graph of the given equation is attached, it shows the linear relationship between both variables.

Notice that the graph is continuous, it doesn't have any restriction, nor "emptyness" at certain values.

Observe that the remaining choices are all solutions of the equation, but not all of them are viable, because the number of cricket chirps
`c` must be positive and integer, because we can't here the sound of 0.5 cricket.

Therefore, the last choice is viable (10, 50).