Section B Section B Checkpoint

Problem 1

A ball attached to a spring bounces up and down. The graph shows $H(t)$ , the height of the ball over a person’s head in inches, as a function of time measured in seconds after the ball is released.

Graph of inches a ball is above a person's head as a function of time after the ball is released

Describe these points on the graph using the situation. Then state whether it is a maximum, minimum, vertical intercept, horizontal intercept, or none of these.

$H(3.7)=0$
$H(4.7) = \text{-}1$

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Solution

Sample responses:

3.7 seconds after the ball is released, it is at the same height as the person’s head. This point is a horizontal intercept.
4.7 seconds after the ball is released, it is 1 inch below the person’s head. This point is a minimum.

Show Sample Response

Sample Response

Sample responses:

3.7 seconds after the ball is released, it is at the same height as the person’s head. This point is a horizontal intercept.
4.7 seconds after the ball is released, it is 1 inch below the person’s head. This point is a minimum.

Problem 2

In a small town with a university, the population changes a lot depending on the season. The population is a function of time represented by $P(t)$ , where $t$ is measured in the number of days after the beginning of the year.

Use function notation to write an expression for the average rate of change for the population of this town from $t = 20$ to $t = 180$ .

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Solution

\frac{P(180)-P(20)}{180-20}

(or equivalent)

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Sample Response

\frac{P(180)-P(20)}{180-20}

(or equivalent)