CPM Homework Help : APCALC Problem 4-110

The three graphs below each tell a story. Examine each graph carefully and then complete each part below. Pay close attention to the labeling of the $x$ - and $y$ -axes.

The graph of $y = s\left(t\right)$ involves a bicycle. Use a complete sentence to describe the physical meaning of $s^\prime\left(6\right)$ . Include units of measure.
Hint (a):
$s'(t)=\frac{ds}{dt}=\text{ instantaneous }\frac{\Delta \text{feet}}{\Delta \text{time}}$

First quadrant, x axis labeled time, hours, y axis labeled distance from home, miles, downward parabola vertex at the approximate point (3.5, comma 6.5), passing through the origin, & passing through the x axis after x = 7.

The graph of $y = r\left(t\right)$ involves an employee of a calculator company. Use a complete sentence to $\int _ { 0 } ^ { 5 } r ( t ) d t$ . Include units of measure.
Hint (b):
$\frac{\text{sales}}{\text{hour}}$
indicates a rate graph and an integral is an area function.
Hint (b):
Be sure to mention the significance of the bounds.

First quadrant, x axis labeled time, hours, y axis labeled rate, sales per hour, increasing curve starting at the origin, concave down, passing through the approximate points (2, comma 3.5), & (6, comma 5).

The graph of $y = w\left(t\right)$ involves a babysitter. Use a complete sentence to describe the physical meaning of $\int _ { 4 } ^ { 10 } w ( i ) d i$ . Include units of measure.
Hint (c):
Refer to the hints in part (b).

First quadrant, x axis labeled time of day, P M, y axis labeled Hourly wage, $ per hour, increasing line starting at the origin, passing through the approximate points (2, comma 3), & (4, comma 7).