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- anonymous

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?

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- anonymous

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- anonymous

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

- 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.

- anonymous

So, wasn't I right then? :)

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- 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.

- zepdrix

blah typos... bust out your calculator*

- anonymous

2.092 is what I got :)

- anonymous

- zepdrix

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

- zepdrix

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

- anonymous

ok :) Hold on.

- anonymous

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

- anonymous

Ok, so for the first part I got 3.32212255

- anonymous

Then 1.25 for the second part

- zepdrix

uhhhhh 0_o

- zepdrix

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

- anonymous

13.389 :)

- anonymous

Thanks<3!!!

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