# Lesson 1

Growing and Shrinking

- Let’s calculate exponential change.

### Problem 1

Select **all** sequences that could be geometric.

2, 4, 7, 11, . . .

\(\frac13\), 1, 3, 9, . . .

1, 3, 5, 7, . . .

\(\frac12\), 2, 8, 32, . . .

1,000, 200, 40, 8, . . .

999, 899, 799, 699, . . .

### Problem 2

A blogger had 400 subscribers to her blog in January. The number of subscribers has grown by a factor of 1.5 every month since then. Write a sequence to represent the number of subscribers in the 3 months that followed.

### Problem 3

Tyler says that the sequence 1, 1, 1,... of repeating 1s is not exponential because it does not change. Do you agree with Tyler? Explain your reasoning.

### Problem 4

In 2000, an invasive plant species covered 0.2% of an island. For the 5 years that followed, the area covered by the plant tripled every year.

A student said, “That means that about half of the island’s area was covered by the plant in 2005!”

Do you agree with his statement? Explain your reasoning.

### Problem 5

A square picture with side length 30 cm is scaled by 60% on a photocopier. The copy is then scaled by 60% again.

- What is the side length of the second copy of the picture?
- What is the side length of the picture after it has been successively scaled by 60% 4 times? Show your reasoning.

### Problem 6

A geometric sequence \(g\) starts 5, 15, . . . . Explain how you would calculate the value of the 50th term.

### Problem 7

Select **all** the expressions equivalent to \(9^4\).

\(3^6\)

\(3^8\)

\(9^2 \times 9^2\)

\(\frac{9^4}{9^{\text-2}}\)

\(3^4 \times 3^4\)