SOLUTION: Hi:) HW question. I have done the first 3 parts successfully, I believe. It's the whole cricket chirping thing. My question is for D). How to find the temp in F when chirping is 40

Question 585316: Hi:) HW question. I have done the first 3 parts successfully, I believe. It's the whole cricket chirping thing. My question is for D). How to find the temp in F when chirping is 40 chirps in 30 seconds (1/2 minute). The first 3 parts are as follows: 68F, 24 chirps/minute. 40F, 86 chirps/minute. A) Express the #chirps as a linear function of the F temp (x). So I wrote, y= -2.214x + 174.552. B) Interpret slope in a sentence. I wrote, for every 1 degree F increase of temp, the # chirps decreases by 2.214 chirps. C) If temp is 60F, how many chirps/minute? I wrote 41.712. (Teacher wants 3 decimal places.) D)If there are 40 chirps in 1/2 minute, what is temp? I have spent soo much time trying to figure this D part but am stuck. I appreciate any help. Thank you.
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
when temp is 68, number of chirps per minute is 24 chirps per minute.
when temp is 40, number of chirps per minute is 86 chirps per minute.
x = degrees Fahrenheit.
y = number of chirps per minute.
PART A:
express as linear equation.
x1,y1 = 68,24
x2,y2 = 40,86
slope of line is (24-86) / (68-40) = -62 / 28 = -2.21428571
slope intercept form of equation is:
y = mx + b
m is slope
b is y intercept.
replace m with -2.21428571 to get:
y = -2.21428571*x + b
replace y with 24 and x with 68 to get:
24 = -2.21428571*68 + b
solve for b to get:
b = 174.5714283
so far so good.
a little off probably due to rounding (you did i didn't).
PART B:
your explanation is good.
you lose 2.214 chirps per minute for every increase of 1 degree.
PART C:
when temp is 60 degrees, number of chirps per minute is equal to:
-2.21428571*60 + 174.5714283 which is equal to 41.71428568.
you're still good.
PART D:
If there are 40 chirps in 1/2 minute, what is temp?
40 chirps in 1/2 minute is equivalent to 80 chirps in 1 minute.
replace y with 80 in your equation and solve for x.
your equation is:
y = -2.21428571*x + 174.5714283
replacing y with 80 gets you:
80 = -2.21428571*x + 174.5714283
subtract 174.5714283 from both sides of this equation to get:
-94.57142828 = -2.21428571*x
divide both sides of this equation by to get -2.21428571 to get x = 42.70967737 degrees.
that's your answer.
x = 42.70967737 which is the number of degrees fahrenheit that will generate 80 chirps per minute based on the equation.
a graph of your equation of:
a horizontal line at y = 80 has been drawn to intersect with a vertical line at x = 42.70967737 to show you where that point would be on the line of the equation.

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