Answer:
[tex]T(N) = \dfrac{14N}{59} + \dfrac{2725}{59}[/tex]
Step-by-step explanation:
We are given the following in the question:
The relation between chirping of crickets and temperature is a linear function.
[tex]T(N) = aN + b[/tex]
where and b are constants. T(N) is the the temperature in Fahrenheit and N is the number of chirps per minute.
"A cricket produces 113 chirps per minute at 73 degrees Fahrenheit"
[tex]73 = 113a+b[/tex]
"A cricket produces 172 chirps per minute at 87 degrees Fahrenheit"
[tex]87 = 172a+b[/tex]
Solving the two equations, we get,
[tex]87-73 = 172a - 113a\\14 = 59a\\\\a =\dfrac{14}{59}\\\\73 = 113(\dfrac{14}{59}) + b\\\\b = 73 - 113(\dfrac{14}{59})\\\\b = \dfrac{2725}{59}[/tex]
Thus, the required linear function is:
[tex]T(N) = \dfrac{14N}{59} + \dfrac{2725}{59}[/tex]
