Question

For her ninth birthday, Isabella’s best friend, Jackson, gave her a full bag of M&M’s. Isabella determined she had 200 M&M’s in the bag. Since Isabella loves candy, she ate half of the M&M’s the first day. Her mom told her if she continues to eat the M&M’s at that rate, they would all be gone by tomorrow. Isabells decided she would only eat half of the candy each day and this would make it last forever!
How much candy does Isabella’s have at the end of 7 days? Will the candy really last forever?


Please include the following information in your final answer:


1. A data table of values

2. Write an equation to represent the data provided in the problem

3. A hand graphed graph of the data table

4. Explain your findings mathematically and compare and contrast them to what you just graphed.

5. Please use complete sentences and thoughts when answering the following questions.


1. Do you think Is

Answer 1

either 1 or 2 would probably work.hope this helps

Answer 2

Answer:

1) 25/8 or 3 1/8  M&Ms 2) No, it won't last forever 3)$y=200*(\frac{1}{2})^{x} }$ 4) The quantity of chocolate decreases exponentially at a rate of 1/2, for a each period of time.

Step-by-step explanation:

This problem works like a Geometric Sequence, whose quotient is 1/2.

Supposing that Isabella has eaten 1/2 and has bee each day eating only half of what's been left.

Setting on a Table:

Day | Candy

1       |  200

2      | 100

3      |  50

4      |  25

5      |  12.5

6      | 6.25

7      |  3.125

$a_{2}=200*(\frac{1}{2})^{1} \\ a_{2}=100\\ a_{3}=200*(\frac{1}{2})^{2}=50\\ a_{4}=200*(\frac{1}{2})^{3}=25\\ a_{5}=200*(\frac{1}{2})^{4}=\frac{25}{2}=12.5 \\ a_{6}=200*(\frac{1}{2})^{5}=\frac{25}{4} =6.25\\ a_{7}=200*(\frac{1}{2})^{6}=\frac{25}{8}=3.125$

2) The equation used is the Recursive Formula for the Geometric Sequence, adjusted to the data:

$y=200*(\frac{1}{2})^{x} }$

3) Check the graph below

4) The quantity of chocolate decreases exponentially at a rate of 1/2, for a each period of time. Each day the amount goes getting smaller and smaller till it gets to zero. Then you can insert more values in the Domain you'll get zero, this is the reason why the curve goes closer and closer until gently intercepts x-axis.