Question

A: Name a situation that is exponential - involves exponents:

B: Write a table out if you have $100 and you gain 5% each year for 3 years:
C: Write a table out if you have $100 and you lose 5% each year for 3 years:
1: What would the ⍰ need to be in the expression below for the simplified form of the expression to be equal to
1 / 8xy^6 ?
4x^2 y^-5 / 2^⍰x^3y
2: Why does the equation 3x^2 - 30 = 3 have two solutions but the equation 3x^2 + 30 = 3 has no solution? Try some different values for x.
3: In the expression below if a = 4, what value of b is needed for the expression to have a value of 81?12a^3b^7 * (ab)^-4
4: A cube has side lengths of 2^5 cm long. If Sam has 16 of these cubes, what total volume would the cubes occupy written as a power of 2? The total volume is 2____ cm3
5: Kelly counted all the doors and wheels on her property. She counted 8^4 doors and 8^2 wheels. How many times more doors are there than wheels?

Answer 1

[AI-generated answer — Bot GPT 3.5]

A: One example of a situation that involves exponents is exponential growth, such as the population of a species doubling every year.

B: Here is a table showing how the amount grows each year with a 5% increase:

Year 1: $100 + $5 (5% of $100) = $105
Year 2: $105 + $5.25 (5% of $105) = $110.25
Year 3: $110.25 + $5.51 (5% of $110.25) = $115.76

C: Here is a table showing how the amount decreases each year with a 5% decrease:

Year 1: $100 - $5 (5% of $100) = $95
Year 2: $95 - $4.75 (5% of $95) = $90.25
Year 3: $90.25 - $4.51 (5% of $90.25) = $85.74

1: The ⍰ would need to be 5 in order for the simplified form of the expression to be equal to 1 / 8xy^6.

2: The equation 3x^2 - 30 = 3 has two solutions because when you solve for x, the quadratic equation has two distinct solutions.
On the other hand, the equation 3x^2 + 30 = 3 has no solution because when you solve for x, the quadratic equation only has complex solutions.

3: If a = 4, the expression becomes 12 * (4^3) * b^7 * (4b)^-4. To make the expression equal to 81, b would need to be 3.

4: The volume of a cube is given by (side length)^3. In this case, the side length is 2^5 cm, so the volume is (2^5)^3 = 2^(5*3) = 2^15 cm^3.
Since Sam has 16 of these cubes, the total volume they occupy would be 16 * 2^15 cm^3.

5: Kelly has 8^4 doors and 8^2 wheels. To find out how many times more doors there are than wheels, we can divide the number of doors by the number of wheels:
(8^4) / (8^2) = 8^(4-2) = 8^2 = 64 times more doors.