The following data were collected by placing a temperature probe in a portable heater, removing the probe, and then recording temperature over time.

Time (sec.) …………………………… Temperature (°F)

0 ….………………………………………… 165.07

1 ….………………………………………… 164.77

2 ….………………………………………… 159.35

3 ….………………………………………… 158.61

4 ….………………………………………… 157.89

5 ….………………………………………… 156.11

6 ….………………………………………… 156.83

7 ….………………………………………… 155.08

8 …..………………………………………… 154.40

9 …..………………………………………… 153.72

10 …………………………………………… 163.99

11 …………………………………………… 163.22

12 …………………………………………… 162.82

13 …………………………………………… 161.96

14 …………………………………………… 161.20

15 …………………………………………… 160.45

According to Newton’s Law of Cooling, these data should follow an exponential model.

(a) Using a graphing utility, draw a scatter diagram for the data.

(b) Using a graphing utility, build an exponential model from the data.

(c) Graph the exponential function found in part (b) on the scatter diagram.

(d) Predict how long it will take for the probe to reach a temperature of 110°F.