Exponential Functions and Age Problems

Mr. Boskin covers various math topics including exponent rules, calculating dimensions of geometric shapes, exponential growth, and solving age-related equations. The video starts with an introduction to exponents, explaining how to multiply them when bases are the same. It then moves on to practical problems involving cubes and squares, followed by a discussion on exponential growth using amoebas as an example. Finally, the video addresses solving equations related to age problems, providing a comprehensive overview of these mathematical concepts.

What is the result of multiplying 10^7 by 10^7?

• 10^7

• 10^49

• 10^21

• 10^14

If you have 10^9 raised to the power of 3, what is the result?

• 10^9

• 10^18

• 10^27

• 10^12

How tall would a tower be if you stacked one million 1-inch cubes?

• 1,000 inches

• 10,000 inches

• 1,000,000 inches

• 100 inches

What would be the side length of a square made from one million square inches?

• 1,000 inches

• 10,000 inches

• 100 inches

• 100,000 inches

If you form a cube from one million 1-inch cubes, what is the side length of the cube?

• 10 inches

• 100 inches

• 1,000 inches

• 10,000 inches

After 6 hours, how many amoebas will there be if they double every hour?

• 128

• 64

• 32

• 256

Why is exponential notation useful for expressing the number of amoebas after 24 hours?

• It's more concise

• It's more visual

• It's easier to calculate

• It's more accurate

Nine years ago, Katie was twice as old as Elena. If Elena is e years old now, what equation represents Katie's age nine years ago?

• k = e + 9

• k = 2(e - 9)

• k - 9 = 2e

• k - 9 = e

In four years, Elena will be as old as Katie is now. If Elena is e years old now, what equation represents this?

• e = k

• e + 4 = k - 4

• e = k + 4

• e + 4 = k

If Elena is 13 years old now, how old is Katie?

• 15

• 17

• 21

• 19