Question

(08.04 MC) Christina bought a yoyo from a company that claims that, with each retraction, the string rolls up by 70% of the original length. She sets up a tape measure and throws the yoyo 3 times. Her data are charted below. Throw Length of string (feet)
1 3
2 2.1
3 1.47

Answers:

9.99
9.72
3.24
0.12

Answer 1

Here is the answer to the given problem. So, what Christina wants to find out is the sum of the length after 10 throws given that in each throw, it retracts 70% of the original length. So to continue the given data, here are the results:
4: 1.029
5: 0.7203
6: 0.50421
7: 0.352947
8: 0.2470629
9: 0.17294403
10: 0.12106082
Since she wants to find the sum of the length after 10 throws, we are just going to add the lengths above. So the answer would be this:  9.71752475. To round this off to the nearest hundredth, the answer would be 9.72. Hope this helps.

Answer 2

Answer: 9.72

Step-by-step explanation: We can use the equation, a1 - a1(r^n)/1 - r

a1 = first term of sequence (3)

r = common ratio (0.70)

n = position of term in sequence (10)

1. 3 - 3(0.70)^10/1 - 0.70

2. 3 - 3(0.0282475)/0.30

3. 3 - 0.0847426/0.30

4. 2.91526/0.30

5. 9.72 is the sum of the lengths.