Lesson 22 Exercises 1–3
1. Predict how many times you can fold a piece of paper in half.
2. Before any folding (zero folds), there is only one layer of paper. This is recorded in the first row of the table.
Fold your paper in half. Record the number of layers of paper that result. Continue as long as possible.
a. Are you able to continue folding the paper indefinitely? Why or why not?
b. How could you use a calculator to find the next number in the series?
c. What is the relationship between the number of folds and the number of layers?
d. How is this relationship represented in the exponential form of the numerical expression?
e. If you fold a paper f times, write an expression to show the number of paper layers.
3. If the paper were to be cut instead of folded, the height of the stack would double at each successive stage, and it would be possible to continue.
a. Write an expression that describes how many layers of paper result from cuts.
b. Evaluate this expression by writing it in standard form.
Example 2: Bacterial Infection
Bacteria are microscopic one-celled organisms that reproduce in a couple of different ways, one of which is called binary fission. In binary fission, a bacterium increases its size until it is large enough to split into two parts that are identical. These two grow until they are both large enough to split into two individual bacteria. This continues as long as growing conditions are favorable.
a. Record the number of bacteria that result from each generation.
b. How many generations would it take until there were over one million bacteria present? c. Under the right growing conditions, many bacteria can reproduce every 15 minutes. Under these conditions, how long would it take for one bacterium to reproduce itself into more than one million bacteria?
d. Write an expression for how many bacteria would be present after g generations.
Example 3: Volume of a Rectangular Solid
This box has a width, w. The height of the box, h, is twice the width. The length of the box, l, is three times the width.That is, the width, height, and length of a rectangular prism are in the ratio of 1:2:3.
For rectangular solids like this, the volume is calculated by multiplying length times width times height.
Why 53 is different from 5 × 3?
Lesson 22 Exit Ticket
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