Question

the speed at which a cricket chirps is affected by the temperature. if a cricket chirps 22 times in 14 seconds, what is the temperature? the temperature is (square^{circ}f). (simplify your answer) number of chirps per 14 seconds 7 12 17 temperature ((^{circ}f)) 47 58 69

Explanation:

Step1: Find slope of linear model

Calculated \(a=\frac{58 - 47}{12 - 7}\)

Step2: Find linear equation

Used point - slope form \(T-47 = 2.2(N - 7)\)

Step3: Substitute \(N = 22\)

Calculated \(T=2.2\times22+31.6\)

Step4: Calculate first term

Found \(2.2\times22 = 48.4\)

Step5: Calculate final temperature

Found \(48.4+31.6 = 80\)

Answer:

We first find the number of chirps per 14 - seconds is 22. We need to find the relationship between chirps per 14 - seconds and temperature from the table.
Let's assume a linear relationship \(T = aN + b\), where \(T\) is the temperature in \(^{\circ}F\), \(N\) is the number of chirps per 14 seconds.
We take two points from the table \((N_1,T_1)=(7,47)\) and \((N_2,T_2)=(12,58)\)
The slope \(a=\frac{T_2 - T_1}{N_2 - N_1}=\frac{58 - 47}{12 - 7}=\frac{11}{5}=2.2\)
Using the point - slope form with the point \((7,47)\): \(T-47 = 2.2(N - 7)\)
\(T-47=2.2N-15.4\)
\(T = 2.2N+31.6\)
When \(N = 22\), \(T=2.2\times22 + 31.6\)

Step1: Calculate \(2.2\times22\)

\(2.2\times22=48.4\)

Step2: Calculate \(48.4+31.6\)

\(48.4 + 31.6=80\)

So the temperature is \(80^{\circ}F\)