Exponential Growth and Dilation Concepts

The video covers Math 8 Unit 7 Lesson 1, focusing on exponents. It begins with a review of exponents, followed by activities that explore exponential growth and decay through stories and practical examples. Students discuss which expression doesn't belong, learn about exponential growth with a genie story, and understand exponential decay with a broken coin. A family tree is used to explain exponents, and the lesson concludes with homework and practice problems to reinforce learning.

Which of the following expressions represents the number of coins on the 6th day if the doubling pattern starts with one coin?

• 2^8

• 2^7

• 2^5

• 2^6

If May's coins double every day for 28 days, what is the expression for the total number of coins on the 28th day?

• 2^28

• 2^25

• 2^26

• 2^27

How many times more coins does May have than Andre if Andre's coins stopped doubling on the 25th day?

• 8 times

• 6 times

• 4 times

• 2 times

What fraction of the coin remains after 6 days if it is halved each day?

• 1/16

• 1/32

• 1/128

• 1/64

Does the coin ever completely disappear if it is halved every day?

• No, it disappears after 50 days

• Yes, after 30 days

• No, it never disappears

• Yes, after 28 days

How many ancestors does Tyler have in the 18th generation?

• 262,144

• 524,288

• 131,072

• 65,536

What is the expression for the amount of money Claire would have after 30 years if she never withdraws from her account?

• 160 * 1.03^5

• 160 * 1.03^10

• 160 * 1.03^30

• 160 * 1.03^15

What does the number 5,280 represent in the equation Y = 5280x?

• Number of feet in a mile

• Number of yards in a mile

• Number of inches in a foot

• Number of miles in a foot

What is the slope of the line passing through the points (2, 4) and (6, 7)?

• 1/2

• 3/4

• 1/3

• 2/3

What is the scale factor for a dilation that reduces a larger triangle to a smaller one?

• 1/5

• 1/3

• 1/2

• 1/4