## anonymous one year ago Finn bought a yoyo from a company that claims that, with each retraction, the string rolls up by 80% of the original length. He sets up a tape measure and throws the yoyo 3 times. His data are charted below. Throw Length of string (feet) 1 3 2 2.4 3 1.92 Finn wants to find the sum of the length of string after 10 throws. What is the sum of the lengths, rounded to the nearest hundredth?

1. anonymous

13.39 feet 15.00 feet <--my answer 4.46 feet 0.40 feet

2. mathmate

With initial length of $$a_1$$=3 feet, and common ratio r= 0.8, the total length of n throws is given by the sum: $$S(n)=a_1(1-r^n)/(1-r)$$ For example, after 1 throw, n=1, S(1)=3(1-0.8)/(1-0.8)=3 feet After 2 throws, $$S(2)=3(1-0.8^2)/(1-0.8)=5.4 feet.$$ You can then calculate S(10) but putting n=10.

3. anonymous

So, wasn't I right then? :)

4. zepdrix

The example mathmate gave,$\large\rm S_2=3\cdot\frac{1-(0.8)^2}{1-0}$As was mentioned though, we want the sum of the first 10,$\large\rm S_{10}=3\cdot\frac{1-(0.8)^{10}}{1-0.8}$So ummmm, yes maybe you are right :o But our your calculator.

5. zepdrix

blah typos... bust out your calculator*

6. anonymous

2.092 is what I got :)

7. anonymous

@zepdrix

8. zepdrix

Hmm you shouldn't get less than 3 -_-

9. zepdrix

$\large\rm S_{10}=3*((1-.8\wedge(10))\div(1-.8))$

10. anonymous

ok :) Hold on.

11. anonymous

That's so weird! Now I got 2.077?? My calculator must be broken..

12. anonymous

Ok, so for the first part I got 3.32212255

13. anonymous

Then 1.25 for the second part

14. zepdrix

uhhhhh 0_o

15. zepdrix

(1-.8^(10))/(1-.8) = 4.463129... And then multiply by 3. I dunno what you're doing there :d weird

16. anonymous

13.389 :)

17. anonymous

Thanks<3!!!