Question

Based on information in Deep River Jim’s Wilderness Trail Book, the rate at which crickets chirp varies linearly with the temperature. At 59o F., they make 76 chirps per minute, and at 65o F., they make 100 chirps per minute.

a) Is this a linear or exponential function?

b) Predict the chirping rate for 70o F. and 100o F.

c) What would you predict the temperature to be if you counted 150 chirps per minute?

Answer 1

a)here as from above statement  rate at which crickets chirp varies linearly with the temperature; therefore it is a linear function

b)

here slope of linear function:b=(Y2-y1)/(x2-x1)=(100-76)/(65-59)=4

and intercept a=(76-59*4)=-160

therfore linear function:y=-160+4x

hence at 70^o F ;  chirping rate =-160+4*70=120

at 100^o F ;  chirping rate =-160+4*100=240

c)

for 150  chirps per minute ; temeperature =(150+160)/4=77.5^o F