SOLUTION: Biologists have observed that the chirping rate of crickets of a certain species is related to temperature and the relationship appears to be very linear. A cricket produces 120 c

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: Biologists have observed that the chirping rate of crickets of a certain species is related to temperature and the relationship appears to be very linear. A cricket produces 120 c      Log On


   

Question 187920: Biologists have observed that the chirping rate of crickets of a certain species is related to temperature and the relationship appears to be very linear. A cricket produces 120 chirps per minute at 80 degrees F and 160 chirps per minute at 85 degress F. If the crickets are chirping at 130 chrps per minute,estimate the temperature. Round to the nearest degree
Answer by jojo14344(1513) About Me  (Show Source):
You can put this solution on YOUR website!


We need to Interpolate the given data to find the unknown temperature.

Given: Chirps per minute = equivalent Temperature in Fahrenheit
(A)120cpm=(D)80F
(B)130cpm=(E) x
(C)160cpm=(F)85F

And we interpolate, %28A-C%29%2F%28A-B%29=%28D-F%29%2F%28D-E%29
%28120-160%29%2F%28120-130%29=%2880-85%29%2F%2880-x%29==>%28-40%29%2F-10=%28-5%29%2F%2880-x%29==>4=%28-5%29%2F%2880-x%29, Cross multiply:
4%2A%2880-x%29=-5==>320-4x=-5, Combine similar terms:
320%2B5=4x==>325=4x==>cross%28325%2981.25%2Fcross%284%29=cross%284%29x%2Fcross%284%29
red%28x=81.25%5Eo%2AF%29 ==> 81 deg.Fahrenheit (rounded)

Thank you,
Jojo