Representing Exponential Growth: IM Alg1.5.3
1. Alg1.5.3 Lesson
1. IM Alg1.5.3 Lesson: Representing Exponential Growth
2. Alg1.5.3 Practice
1. IM Alg1.5.3 Practice: Representing Exponential Growth

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Representing Exponential Growth: IM Alg1.5.3

GeoGebra Classroom Activities, Feb 17, 2021

[url=https://im.kendallhunt.com/HS/teachers/1/5/3/preparation.html]“Representing Exponential Growth”[/url] from IM Algebra I © 2019 [url=https://www.illustrativemathematics.org/]Illustrative Mathematics[/url]. Licensed under the [url=https://creativecommons.org/licenses/by/4.0/]Creative Commons Attribution 4.0[/url] license.

Alg1.5.3 Lesson
1. IM Alg1.5.3 Lesson: Representing Exponential Growth
Alg1.5.3 Practice
1. IM Alg1.5.3 Practice: Representing Exponential Growth

1.

Alg1.5.3 Lesson

1. IM Alg1.5.3 Lesson: Representing Exponential Growth

1.1.

IM Alg1.5.3 Lesson: Representing Exponential Growth

Rewrite each expression as a power of 2.

[math]2^3\cdot2^4[/math]

[math]2^5\cdot2[/math]

[math]2^{10}\div2^7[/math]

[math]2^9\div2[/math]

Complete the table. Take advantage of any patterns you notice.

[size=150]Here are some equations. Find the solution to each equation using what you know about exponent rules. Be prepared to explain your reasoning.[/size][br][br][math]9^?\cdot9^7=9^7[/math]

[math]\frac{9^{12}}{9^?}=9^{12}[/math]

What is the value of [math]5^0[/math]? [br][br]

What about [math]2^0[/math]?

[size=150]We know, for example, that [math]\left(2+3\right)+5=2+\left(3+5\right)[/math] and [math]2\cdot\left(3\cdot5\right)=\left(2\cdot3\right)\cdot5[/math]. The grouping with parentheses does not affect the value of the expression.[br][/size][br][size=100]Is this true for exponents? That is, are the numbers [math]2^{\left(3^5\right)}[/math] and [math]\left(2^3\right)^5[/math] equal? If not, which is bigger? [/size]

Which of the two would you choose as the meaning of the expression [math]2^{3^5}[/math] written without parentheses?

In a biology lab, 500 bacteria reproduce by splitting. Every hour, on the hour, each bacterium splits into two bacteria.

Write an expression to show how to find the number of bacteria after each hour listed in the table.

Write an equation relating [math]n[/math], the number of bacteria, to [math]t[/math], the number of hours.[br]

[size=150][size=100]Use your equation to find [math]n[/math] when [math]t[/math] is 0. [/size][/size]What does this value of [math]n[/math] mean in this situation?[br]

[size=150]In a different biology lab, a population of single-cell parasites also reproduces hourly. An equation which gives the number of parasites, [math]p[/math], after [math]t[/math] hours is [math]p=100\cdot3^t[/math]. [/size][br]Explain what the numbers 100 and 3 mean in this situation.[br]

Refer back to your work in the table of the previous task. Use that information and the given coordinate planes to graph the following: Graph (t, n) when t is 0, 1, 2, 3, and 4.

Graph (t, p) when t is 0, 1, 2, 3, and 4. (If you get stuck, you can create a table.)

On the graph of [math]n[/math], where can you see each number that appears in the equation?[br]

On the graph of [math]p[/math], where can you see each number that appears in the equation?[br]

2.

Alg1.5.3 Practice

1. IM Alg1.5.3 Practice: Representing Exponential Growth

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Representing Exponential Growth: IM Alg1.5.3

Table of Contents

1.

Alg1.5.3 Lesson

1.1.

IM Alg1.5.3 Lesson: Representing Exponential Growth

Rewrite each expression as a power of 2.

Complete the table. Take advantage of any patterns you notice.

In a biology lab, 500 bacteria reproduce by splitting. Every hour, on the hour, each bacterium splits into two bacteria.

Refer back to your work in the table of the previous task. Use that information and the given coordinate planes to graph the following: Graph (t, n) when t is 0, 1, 2, 3, and 4.

Graph (t, p) when t is 0, 1, 2, 3, and 4. (If you get stuck, you can create a table.)

2.

Alg1.5.3 Practice

2.1.

IM Alg1.5.3 Practice: Representing Exponential Growth

A bee population is measured each week and the results are plotted on the graph.

A bond is initially bought for $250. It doubles in value every decade. Complete the table.

Bank account A starts with $5,000 and grows by $1,000 each week. Bank account B starts with $1 and doubles each week.

Match each equation in the first list to an equation in the second list that has the same solution.

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