Question

Jessa bought a yoyo from a company that claims that, with each retraction, the string rolls up by 60% 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 1.8 3 1.08 Jessa 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

Answer: 7.45 feet

Explanation:

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Answer 2

The sum is 7.45

Explanation:

Every time she throws a yoyo, the new length is 60% of the original, so we can calculate the length of the yoyo in the n throw as:

`L_1=3(0.6)^(0)=3\\L_2=3(0.6)^(1)=1.8\\L_3=3(0.6)^(2)=1.08\\L_n=3(0.6)^(n-1)`

Then, the sum of the n terms is a geometric serie because every term has the form:

`a(r)^(n-1)`

Where a is equal to 3, r is equal to 0.6 and n goes from 1 to 10

Therefore, the sum of the n terms can be calculated as:

`S_n=a*(1-r^(n) )/(1-r) \\`

So, the sum of the length of string after 10 throws is:

`S_(10)=3*(1-0.6^(10) )/(1-0.6)=7.45 \\`