### Home > CALC > Chapter 1 > Lesson 1.2.4 > Problem 1-74

A can of soda is 42°F when purchased. Over the course of the next few hours, the temperature of the

soda slowly rises. During an experiment, Shibisha used a thermometer and recorded the temperature at various times, *t*, shown in the table below. 1-74 HW eTool (Desmos). Homework Help ✎

**time(min)**0

10

30

45

60

75

80

**temp (°F)**42

51

58

63

66

68

69

Sketch a graph of this temperature over time.

When is the temperature changing the fastest? How does the graph tell you this?

Approximately how fast is the temperature changing during the first 10 minutes? How can you tell?

First plot the data. Then connect the points as smoothly as possible. How do we know that this will be a continuous graph?

Consider the relationship between rates of change and slope. Between which two points is the slope the greatest?

Use the eTool below to view the graph.

Click the link at right for the full version of the eTool: Calc 1-74 HW eTool