CPM Homework Help : CALC 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. .

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.
Graph (a):
First plot the data. Then connect the points as smoothly as possible. How do we know that this will be a continuous graph?
When is the temperature changing the fastest? How does the graph tell you this?
Hint (b):
Consider the relationship between rates of change and slope. Between which two points is the slope the greatest?
Approximately how fast is the temperature changing during the first $10$ minutes? How can you tell?

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