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Question 1075432: I've been stuck on these problems, I've figured out parts of each question but need help with it!
When the SuperBall® was introduced in the 1960’s, kids across the United
States were amazed that these hard rubber balls could bounce to 90% of the
height from which they were dropped.
a. Is this problem an example of a geometric series or an
arithmetic series? Support your answer mathematically by applying the
concepts from this unit.
b. If a SuperBall® is dropped from a height of 2m, how far does it
travel by the time it hits the ground for the tenth time? (Hint: The ball
goes down to the first bounce, then up and down thereafter.)
To figure this problem out, one way I would solve this problem is to use
the formula An=2 (.90)^n-1 , then to get a11 we plug in the info we know,
to get 2(.9)^10 to get an answer of aout .70m
2. You borrowed $5,000 from your parents to purchase a used car.
You have agreed to make payments of $250 per month plus an additional 1%
interest on the unpaid balance of the loan.
a. Is this problem an example of a geometric series or an
arithmetic series? Support your answer mathematically by applying the
concepts from this unit.
b. Find the first year’s monthly payments that you will make and
the unpaid balance after each month.
c. Find the total amount of interest paid over the term
of the loan
Thanks!
Answer by Boreal(15235)   (Show Source):
You can put this solution on YOUR website! The fact that the amount changes each bounce makes it a geometric series.
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I am assuming no interest on the loan other than the 1% unpaid balance.
After 1 month $4750 +47.50=4797.50
after 2: 4547.50+45.48=4592.98
3:4342.98+43.43=4386.41
4:4136.41+41.36=4177.77
5:3927.77+39.28=3966.05
6:3716.05+37.16=3753.21
7:3503.21+35.03=3538.24
8:3288.24+32.88=3321.12
9:3071.12+30.71=3101.83
10:2751.83+27.52=2779.35
11:2529.35+25.29=2554.64
12:2304.64+23.05=2327.69
13:2077.69+20.79=2098.46
14:1848.96+18.49=1867.45
15:1617.45+16.17=1633.62
16:1383.62+13.84=1397.46
17:1147.96+11.48=1159.44
18:899.44+8.99=908.43
19:658.43+6.58=665.01
20:415.01+4.15=419.16
21:169.06+1.69=170.65
This is geometric series--rate of change is proportional to the amount, not fixed.
Interest over loan is
$530.87
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