Carlos pours a cup of hot coffee, but then forgets about it and leaves it sittin
ID: 3102422 • Letter: C
Question
Carlos pours a cup of hot coffee, but then forgets about it and leaves it sitting on the ocuner. AS time goes by, the coffee cools off. An equation to model this drop in temperature is:y= 80x + 300/ x + 2
here x = the number of minutes since carlos poured the coffee (x >= 0),
y = the temperature of the coffee in the cup ( in degrees fahrenheit)
8. about how hot was the coffeee 1 minute after it was poured?
9. What would be the approx. temp. of the coffee 2 hours after it is poured.
10. Set up and solve an equation to determine how many minutes it would take for the coffee in the cup to reach a temperature of 85 deg. F
Explanation / Answer
8. Since x is the number of minutes, you plug in 1 for your x value and solve for y, the temperature.
y= 80(1) + 300 /(1+2) = 830/3 = 276.7 F
Seems kind of high but that's what the formula says.
9. When two hours go buy you do the same thing as above. Except you have to convert 2 hours to minutes since the x value is in minutes. 2 hours X (60min/hour) = 120 minutes.
y= 80(120) +300 / (120+ 2) = 9900/122 = 81.1 F
10. Now instead of finding the temperature your finding the amount of minutes. So this time your going to solve for x instead of y.
Plug in 85 for y and solve for x:
85= 80x + 300 / (x+2)
Mulitply the entire denominator to the other side to get:
85(x+2) = 80x +300
Then distribute the 85:
85x + 170 = 80x+300
Simplify the x values (85x-80x = 5x)
5x + 170 = 300
Simplify the constants ( 300-170 = 130)
5x = 130
Solve for x:
x= 130/5 = 26 minutes.
The reason it may seem odd for it to take 120 minutes to reach 81 F and only 26 to reach 85 F is because as the temperature of the coffee comes closer to equillibrium, the coffee cools at a much slower rate.