Question

12. The number of chirps that a cricket produces varies directly with the temperature. Theequation ;= 5x30 approximates that situation, where x represents the temperature irdegrees Celsius and y represents the numer of chirps produced in one minute. Whichexpression is an appropriate range for the number of chirps, y, if –30

Answer 1

Step 1:

We are to find an appropriate expresson for the range for the number of Chirps.

Step 2;

The equation given is y = 5x - 30

The range of x given;

`-30\text{ }\leq\text{ x }\leq\text{ 44}`

Step 3:

We substitute both the lowest and greatest value into the equations;

`\begin{gathered} y\text{ = 5x -30} \\ \text{when x = -30} \\ y\text{ = 5 (-30) - 30} \\ y\text{ = -150 - 30} \\ y\text{ = -180} \end{gathered}`
`\begin{gathered} y\text{ = 5x - 30} \\ \text{when x = 44} \\ y\text{ = 5 (44) - 30} \\ y\text{ = 220 - 30} \\ y\text{ = 190} \end{gathered}`

Step 4:

It is very obvious that the number of Chirps can never be negative so we need to ignore the -180 and set our range to start from zero.

We now have;

`0\text{ }\leq\text{ y }\leq\text{ 190}`