Answer:
a. The expression that represents the number of cups of hot chocolate drunk per day as a function of degrees Celsius is
y = -30x + 3600 pr the equivalent y = 3600 - 30x
b. How many cups would they drink at 5 degrees Celsius?
x = 5 --> y = 3600 - 30 X 5 --> y = 3600 - 150 --> y = 3450
c. How many cups would they drink at 25 degrees Celsius?
x = 25 --> y = 3600 - 30 X 25 --> y = 3600 - 750 --> y = 2850
d. Write an equation to determine the temperature if 3000 cups of hot chocolate were consumed in a day.
y = 3000 --> 3000 = 3600 - 30x
e. Solve the equation to find the temperature if 3000 cups of hot chocolate were consumed in a day.
--> 3000 = 3600 - 30x --> 3000 - 3000 + 30x = 3600 - 30x - 3000 + 30x --> 30x + 600 --> 30x/30 = 600/30 --> x = 20
f. Is this answer reasonable? Explain.
It is very reasonable.
At 0 degree C. they drink 3600 cups.
As the temperature increases, hot chocolate consumption decreases.
At 5 degree C. they drink less hot chocolate: 3450 cups.
Since 20 degree C. is even warmer, they should drink even less at 20 degree C., but not as little as the 2850 cups they drink on those very warm 25 degree C. days.
Step-by-step explanation:
We need to name/define variables:
y = number of cups of hot chocolate consumed in a day in Fairbanks.
x = temperature in degrees Celsius
"For each rise of 1 degrees Celsius, their consumption decreases by 30 cups per day."
That tells you that y is a linear function of x, so we should be able to write it as
y=mx + b with some constants for slope, m, and y-intercept, b.
It also tells you that the slope is m=-30.
"People living in Fairbanks drink 3600 cups of hot chocolate per day when the temperature is 0 degrees Celsius."
That gives you the value of y when x=0, which is the y-intercept,
b=3600
