Question

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?

Answer 1

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

Answer 2

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.

Answer 3

So, wasn't I right then? :)

Answer 4

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.

Answer 5

blah typos... bust out your calculator*

Answer 6

2.092 is what I got :)

Answer 7

@zepdrix

Answer 8

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

Answer 9

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

Answer 10

ok :) Hold on.

Answer 11

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

Answer 12

Ok, so for the first part I got 3.32212255

Answer 13

Then 1.25 for the second part

Answer 14

uhhhhh 0_o

Answer 15

(1-.8^(10))/(1-.8) = 4.463129...

And then multiply by 3.

I dunno what you're doing there :d weird

Answer 16

13.389 :)

Answer 17

Thanks<3!!!