Erin is a biology student. She heard that the number of times a cricket chirps in one minute can be used to find the temperature. In an experiment, she finds that a cricket chirps 40 times per minute when the temp. is 50 degrees(Fahrenheit) and 80 times per minute when the temp. is 60 degrees. Find the temp. when the cricket chirps at 95 times per min.
on the assumption that this relation is linear,
you can treat this as being given two ordered pairs in the relation, namely
(40,50 and (80,60), where the first variable is c (chirps) and the second variable is t (time)
so we are looking for t = mc + b (to resemble the familiar y = mx + b linear equation)
slope = (60-50)/(80-40) = 10/40 = 1/4
using m= 1/4 and the point (40,50)
50 = (1/4)(40) + b
b = 40
so you have t = 1/4c + 40
when c = 95
t = (1/4)(95) + 40
= 63.75 degrees
OR
draw a straight line, plot the points
(40,50), (80,60) and (95,t)
then (t-60).(95-80) = (60-5)/(80-40)
(t-60)/15 = 1/4
4t - 240 = 15
t = 63.75
To find the temperature when the cricket chirps at 95 times per minute, we can use a simple linear equation. Let's assume that the relationship between the temperature (T) and the number of chirps per minute (N) can be represented by the equation:
N = aT + b
where 'a' and 'b' are coefficients to be determined.
Using the given data points, we can set up two equations:
1) When T = 50 degrees and N = 40 chirps per minute:
40 = 50a + b
2) When T = 60 degrees and N = 80 chirps per minute:
80 = 60a + b
We can solve this system of linear equations to find the values of 'a' and 'b'.
Subtracting equation 1 from equation 2, we get:
80 - 40 = 60a + b - 50a - b
40 = 10a
Dividing both sides by 10, we find:
a = 4
Substituting the value of 'a' into either equation 1 or 2, we can solve for 'b'. Let's use equation 1:
40 = 50a + b
40 = 50(4) + b
40 = 200 + b
b = 40 - 200
b = -160
Now that we have the values of 'a' and 'b', we can substitute them into the equation N = aT + b to find the temperature (T) when the cricket chirps 95 times per minute:
95 = 4T - 160
Adding 160 to both sides, we have:
95 + 160 = 4T
255 = 4T
Dividing both sides by 4, we find:
T = 255/4
T = 63.75 degrees Fahrenheit
Therefore, when the cricket chirps at 95 times per minute, the approximate temperature is 63.75 degrees Fahrenheit.