(a)

Graph the data model:

From the table values using graphing utility graph the data model.

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Observe the graph:

The model form of the data is .

Where is temperature, is time in months and corresponds to january.

(b)

Using graphing utility to graph the model. How well does the model fit the data.

Graph the function: .

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(c) Find and use a graphing utility to graph the derivative.

Apply derivative on each side with respect to .

.

Graph the function:.

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Observe the rate of chane of temperature graph.

The temperature changes most rapidly when , so in April

The most slowly when so when or  .

(a) .

(b)

Graph the function: .

.

(c) .

Graph the function:.

.

(d)

The temperature changes most rapidly when , so in April

The most slowly when so when or  .(july and january).