Exponential Growth and Coin Doubling

The video tutorial covers Lesson 12, where students are presented with a choice between $50,000 and a magical coin that doubles in value daily for 28 days. The lesson explains the concept of exponents and how to calculate the value of the coins over time. It demonstrates how to determine when the coin value exceeds $50,000 and $1,000,000. The tutorial also includes exercises on finding expressions that equal 16 and 81 using exponents.

What choice does the genie offer in the problem?

• A fixed sum of $100,000 or a magical $1 coin

• A fixed sum of $50,000 or a magical $1 coin

• A fixed sum of $10,000 or a magical $1 coin

• A fixed sum of $5,000 or a magical $1 coin

How many coins are there on the third day?

• 4 coins

• 6 coins

• 8 coins

• 10 coins

What does 2 to the 5th power represent in the context of the problem?

• The number of coins on the 4th day

• The number of coins on the 5th day

• The number of coins on the 6th day

• The number of coins on the 7th day

On which day does the number of coins first exceed 50,000?

• 15th day

• 17th day

• 16th day

• 14th day

Does the value of the magical coin exceed a million dollars within 28 days?

• Yes, on the 20th day

• Yes, on the 25th day

• No, it never exceeds a million

• Yes, on the 28th day

Which of the following expressions does NOT equal 16?

• 8^2

• 2^4

• 4^2

• 8 * 2

Which expression equals 81?

• 4^3

• 9^2

• 3^3

• 2^6

How many threes are needed to make 81?

• Four threes

• Two threes

• Three threes

• Five threes

What is the result of 3^4?

• 64

• 81

• 27

• 16

What should you consider when choosing between the fixed sum and the magical coin?

• The initial value of the coin

• The doubling rate of the coin

• The number of days the coin doubles

• All of the above