Question

Biologists have observed that the chirping rate of crickets of a certain species is related to temperature, and the relationship appears to be very nearly linear. A cricket produces 120 chirps per minute at 70°F and 168 chirps per minute at 80°F.
(a) Find the linear equation that relates the temperature t and the number of chirps per minute n.




(b) If the crickets are chirping at 138 chirps per minute, estimate the temperature. (Round your answer to the nearest degree.)

Answer 1

Hmm based on the way they worded part b, it sounds like they want you to write this equation as a function of Temperature --> n(t)

So we need to find a linear equation to model this.
It will be of the form n(t)=mt+b
to find m:
\[m=\frac{ y_2 - y_1 }{ x_2 - x_1 }\]\[m=\frac{ n_2 - n_1 }{ t_2 - t_1 }\]
Let's get our data into ordered pairs and find the slope.

Answer 2

mm i did that backwards, i meant a function of chirps lol... crap :D

Answer 3

10/48= 5/24

Answer 4

it'll stil work out fine though :)

Answer 5

did you put chirps or temperature on top? :o

Answer 6

you put temperature, thats fine, lets just rewrite our formula in terms of chirps then :)
\[t(n)=mn+b\]

Answer 7

so we found our m, the slope of our function.
m=5/24
\[t(n)=\frac{ 5 }{ 24 }n+b\]

plug in one of your coordinate pairs to find a b value :D

Answer 8

168=5/24n+80

Answer 9

woops, you plugged 80 in for b.
our ordered pair is of the form (n,t)

Answer 10

im confused please show me

Answer 11

t(n)=(5/24)n+b plugging in (n,t(n)) which is (168, 80)

-> 80=(5/24)(168)+b

Answer 12

ok?

Answer 13

solve for b :)

Answer 14

b=45

Answer 15

yay good! :) ok we have an equation for the line
\[t(n)=(5/24)n+45\]

now lets use that equation to find the temperature when the number of chirps per minute is 138.
\[t(138)=(5/24)(138)+45\]

Answer 16

do i have to put t(n) or can i just put n

Answer 17

? :o

Answer 18

t(n) is our function output, its similar to f(x), it's our y variable.
It's not the same as n, if that's what you were asking <:o

Answer 19

what about just putting t instead of t(n) im trying to enter it on an online hw thing

Answer 20

oh i see, yah try t=(5/24)n+45

Answer 21

Thanks :)

Answer 22

yay gj, were you able to get an answer for b also?

Answer 23

yes :)