When they dial 3 and turn the oven on, it is like pushing the old button 3 times. That means if they start with one pizza in the oven, dial 3, and turn the oven on, they will get 27 pizzas. (33 = 27)
Then if they dial -3 and turn the oven on it is like flicking the old switch three times. If they started with one whole pizza, dialed –3, and turned the oven on, they would get of a pizza. (3–3 =)
The advantage is they can dial numbers, both positive and negative that are not integers. If they start with one whole pizza, dial and turn the oven on, you saw in class they got about 1.73 pizzas. (31/2 ≈ 1.73)
a. If they start with 1 whole pizza, what should they dial, so they come out with 10 pizzas after they turn the oven on. (Hint. Between what whole numbers should they set the dial? You’ll need to guess several numbers and check on your calculator. See how close you can get to 10. )
b. They are expecting a BIG party. If they put one pizza in the oven, what should they dial so they will have 100 pizzas after they turn the oven on? How should your answer to this question relate to your answer in part (a)?
c. If they start with one pizza what should they dial to get 1000 pizzas?
d. If they start with one pizza what should they dial to get of a pizza?
setting the switch on n produces 3^n pizzas
3^2.096 = 10
3^4.192 = 100
3^6.288 = 1000
d. ?
To find the answer to these questions, we need to understand the relationship between the dial number and the resulting number of pizzas in the oven.
Let's break down the given information step by step:
1. If they dial 3 and turn the oven on, it is like pushing the old button 3 times. This means the resulting number of pizzas is obtained by multiplying the initial number of pizzas by 3. For example, if they start with one pizza and dial 3, they will have 3 * 1 = 3 pizzas.
2. Similarly, if they dial -3 and turn the oven on, it is like flicking the old switch three times. This means the resulting number of pizzas is obtained by dividing the initial number of pizzas by 3. For example, if they start with one pizza and dial -3, they will have 1 / 3 = 0.33 (approximately) of a pizza.
3. They can also dial numbers that are not integers. For instance, if they start with one pizza and dial 1/2, they get 1 * (1/2) = 0.5 (approximately) pizzas.
Now let's answer the given questions:
a. If they start with 1 whole pizza and want to end up with 10 pizzas, they should set the dial number somewhere between two whole numbers. To find the closest possible dial number, you will need to guess several numbers and check using a calculator. Start by trying numbers that are slightly less than their target and gradually increase until you reach a number that results in approximately 10 pizzas.
For example, start with a dial number of 2: 1 * 2 = 2 pizzas. Not enough.
Try a dial number of 3: 1 * 3 = 3 pizzas. Still not enough.
Continue this process until you find a dial number that gets you close to 10 pizzas after turning the oven on. Repeat the process with decimal numbers if necessary.
b. If they start with 1 pizza and want to end up with 100 pizzas, they should follow a similar procedure as in part a. Keep trying different dial numbers, increasing from 2, and test them using a calculator until you find a number that results in approximately 100 pizzas.
Your answer to this question should help you understand the relationship between the dial numbers and the resulting number of pizzas. You can use this understanding to make an educated guess and minimize the number of attempts needed to find the right dial number.
c. If they start with 1 pizza and want to end up with 1000 pizzas, you should apply the same method as in part a and b. Explore dial numbers greater than 2 and test them using a calculator until you find a number that results in approximately 1000 pizzas.
d. If they start with 1 pizza and want to end up with 1/3 (one-third) of a pizza, they should set the dial number to -3. As mentioned earlier, dialing -3 is like flicking the old switch three times, which is equivalent to dividing the initial number of pizzas by 3. Thus, 1 / 3 = 0.33 (approximately) of a pizza.
Remember to always use a calculator to verify your results and make sure to perform the calculations accurately.