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When a person is swinging the amplitude (the swings"s distance above it's rest position) increases with each pump. According to Scientific magazine the amplitude increases by adding a constant when the person pumps sitting down, and by multiplying by a constant when the person pumps standing up. Suppose that when you get on a swing, its amplitude is 3cm (ie t(sub 0) =3). Assume that the amplitude increases by 2 cm each pump when you are sitting, and increases by multiplying by 1.2 each pump when you are standing.

a. what is your amplitude after 20 pumps if you are standing? If you are sitting?
b. What is the minimum number of pumps needed to make the amplitude equal 75 cm when you pump sitting down? Standing up?

• math -

sitting: a = 3+2p for p pumps
standing: a = 3*1.2^p for p pumps

3+2(20) = 43
3*1.2^20 = 115

3+2p = 75: p=36
3*1.2^p = 75: p=18

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