# Lesson 3

Representing Exponential Growth

Let’s explore exponential growth.

### Problem 1

Which expression is equal to \(4^0 \boldcdot 4^2\)?

0

1

16

64

### Problem 2

Select **all ** expressions are equivalent to \(3^{8}\).

\(8^3\)

\(\frac{3^{10}}{3^2}\)

\(3 \boldcdot 8\)

\(\left(3^4\right)^2\)

\(\left(3\boldcdot 3\right)^4\)

\(\frac{1}{3^{\text-8}}\)

### Problem 3

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

- What is the bee population when it is first measured?
- Is the bee population growing by the same factor each week? Explain how you know.
- What is an equation that models the bee population, \(b\), \(w\) weeks after it is first measured?

### Problem 4

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

- Complete the table.
- How many decades does it take before the bond is worth more than $10,000?
- Write an equation relating \(v\), the value of the bond, to \(d\), the number of decades since the bond was bought.

decades since bond is bought |
dollar value of bond |
---|---|

0 | |

1 | |

2 | |

3 | |

\(d\) |

### Problem 5

A sea turtle population \(p\) is modeled by the equation \(p = 400 \boldcdot \left(\frac{5}{4}\right)^y\) where \(y\) is the number of years since the population was first measured.

- How many turtles are in the population when it is first measured? Where do you see this in the equation?
- Is the population increasing or decreasing? How can you tell from the equation?
- When will the turtle population reach 700? Explain how you know.

### Problem 6

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

- Which account has more money after one week? After two weeks?
- Here is a graph showing the two account balances. Which graph corresponds to which situation? Explain how you know.
- Given a choice, which of the two accounts would you choose? Explain your reasoning.

### Problem 7

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

### Problem 8

Function \(F\) is defined so that its output \(F(t)\) is the number of followers on a social media account \(t\) days after set up of the account.

- Explain the meaning of \(F(30) = 8,\!950\) in this situation.
- Explain the meaning of \(F(0) = 0\).
- Write a statement about function \(F\) that represents the fact that there were 28,800 followers 110 days after the set up of the account.
- Explain the meaning of \(t\) in the equation \(F(t) = 100,\!000\).