10. (8 pts) (extra credit at the end) EXPONENTIAL REGRESSION Data: A cup of hot

Question

10. (8 pts) (extra credit at the end) EXPONENTIAL REGRESSION Data: A cup of hot coffee was placed in a room maintained at a constant temperature of 73 degrees, and the coffee temperature was recorded periodically, in Table TABLE 1 REMARKS: Common sense tells us that the coffee will be cooling off and its temperature will decrease and approach temperature of the room, 73 degrees. TABLE 2 -C-73 Temperature the ambient t = Time ElapsedDifference t= Time | Coffee ElapsedTemperature (minutes) (de minutes 0 10 20 30 So, the temperature difference between the coffee 97.0 71.5 56.2 41.3 35.5 29.4 24.9 170.0 temperature and the room temperature will decrease to 0. 144.5 12971 We will fit the temperature difference data (Table 2) to an 114.3 exponential curve of the form y-A e 10 30 108.5 Notice that as t gets large, y will get closer and closer to 0, 102.4 which is what the temperature difference will do. 979 | So, we want to analyze the data where time elapsed 50 60 and y C-73, the temperature difference between the coffee temperature and the room temperature 120 Temperature Difference between Coffee and Roonm 100 8 80 y = 89·976e-o.023t 60 20 30 50 60 70 Time Elapsed (minutes) Exponential Function of Best Fit (using the data in Table 2): y = 89.976 e-Q0231 W where t = Time Elapsed (minutes) and-Temperature Difference (in degrees) (a) Use the exponential function to estimate the temperature difference y when 35 minutes have elapsed. Report your estimated temperature difference to the nearest tenth of a degree. (explanation/work optional)

Explanation / Answer

y = 89.976 e^-.023t

a) temperature difference when 35 minutes have elapsed

plug t = 35

y = 89.976 e^-.023(35) = 40.20 degree

b) estimated coffee temperature is 40.20 + 73 = 113.20 degrees

c) when coffee temperature = 140 degrees

y = C - 73 = 140 - 73 = 67 degrees

d) consider the equation y = 89.976 e^-.023t when y = 67 degrees

Related Questions

Navigate

• Browse (All)
• Browse 1
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.