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Problem 10

# Calculate the average rate of change of the given function over the given interval. Where appropriate, specify the units of measurement. HINT [See Example 1.] $$\text { Cisco Systems Stock Price (\) }$$$$\text { Interval: }[1,5]$$

Expert verified
The short answer to the question is: The average rate of change of the Cisco Systems Stock Price over the interval [1, 5] is given by $$\frac{P(5)-P(1)}{4}$$ dollars per day, where P(1) represents the stock price at t=1 and P(5) represents the stock price at t=5.
See the step by step solution

## Step 1: Find the stock price at the given interval end points

We are given the interval [1, 5]. We need to find the stock prices at these points. Let the stock price at t=1 be P(1) and at t=5 be P(5).

## Step 2: Formula for average rate of change

The formula for the average rate of change of a function over an interval [a, b] is given by: $$\text{Average Rate of Change} = \frac{P(b)-P(a)}{b-a}$$ In our case, a = 1 and b = 5. We will plug these values into the formula to find the average rate of change.

## Step 3: Calculate the average rate of change

Now, let's plug in the values of P(1) and P(5) into the formula: $$\text{Average Rate of Change} = \frac{P(5)-P(1)}{5-1}$$ Simplify the denominator: $$\text{Average Rate of Change} = \frac{P(5)-P(1)}{4}$$

## Step 4: Interpret the result

The average rate of change represents the average increase or decrease in the stock price over the given interval. This means the stock price increased or decreased by this amount per day (since the interval is given in days) on average within the specified period. The units of measurement are dollars per day.

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