Lesson 2 Shh! Please Be Discreet (Discrete)! Solidify Understanding

Ready

In problems 1–4, the work to find the slope in each representation has been started. Your job is to finish finding the slopes and show whether or not the slopes are the same for the pairs of representations provided.

1.

Slope =

Slope =

Is the slope the same in each? Why?

2.

Slope =

Slope =

Is the slope the same in each? Why?

3.

Slope =

Slope =

Is the slope the same in each? Why?

4.

Slope =

Slope =

Is the slope the same in each? Why?

Set

For problems 5–10, create a graphical model based on the context. Indicate if the relationship is linear or exponential and if the context is best modeled as discrete or continuous.

5.

The freeway construction crew pours $300 feet$ of concrete in a day.

a.

Graphical model:

b.

Linear or exponential, discrete or continuous?

6.

For every hour that passes, the amount of area infected by the bacteria doubles.

a.

Graphical model:

b.

Linear or exponential, discrete or continuous?

7.

To meet the demands placed on them, the brick layers have started laying $5 %$ more bricks each day.

a.

Graphical model:

b.

Linear or exponential, discrete or continuous?

8.

The average person takes $10,000 steps$ in a day.

a.

Graphical model:

b.

Linear or exponential, discrete or continuous?

9.

The city of Buenos Aires has been adding $8 %$ to its population every year.

a.

Graphical model:

b.

Linear or exponential, discrete or continuous?

10.

At the headwaters of the Mississippi River, the water flows at a surface rate of $1.2 miles per hour$ .

a.

Graphical model:

b.

Linear or exponential, discrete or continuous?

For problems 11–13, a mathematical representation is provided. State whether the context it describes is discrete or continuous. Identify if it is linear (arithmetic) or exponential (geometric). Finally, create a context or story that connects with each representation.

11.

$f (n) = f (n - 1) + 3; f (1) = 5$

12.

13.

$g (x) = 2^{x} (7)$

Go

Solve the following equations. Show your work.

Example: Solve for $x$ . $x + 7 = 23$ . Add $- 7$ to both sides of the equation.

$\begin{array}{rcr} x + 7 & = & 23 \\ \underset{―}{- 7} & \underset{―}{- 7} \\ x + 0 & = & 16 \end{array}$

Therefore, $x = 16$

Example: Solve for $x$ . $9 x = 63$ . Multiply both sides of the equation by $\frac{1}{9}$ .

$\begin{array}{rcl} 9 x & = & 63 \\ \frac{1}{9} (9 x) & = & \frac{1}{9} (63) \\ \frac{9}{9} x & = & \frac{63}{9} \\ x & = & 7 \end{array}$

Note that multiplying by $\frac{1}{9}$ gives the same result as dividing everything by $9$ .

14.

$1 x + 16 = 36$

15.

$425 x = 850$

16.

$\frac{1}{6} x = 10$

17.

$- \frac{4}{7} x = - 1$

Find the recursive and explicit equations for the sequences in the tables.

18.

Term	Value
$1$	$20$
$2$	$16$
$3$	$12$
$4$	$8$

19.

Term	Value
$1$	$9$
$2$	$18$
$3$	$36$
$4$	$72$

20.

Term	Value
$6$	$20$
$7$	$60$
$8$	$180$
$9$	$540$

21.

Term	Value
$4$	$10$
$5$	$20$
$6$	$30$
$7$	$40$