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One lucky day, you meet a leprechaun who promises to give you fantastic wealth, but hands you only a penny before disappearing. You head home and place the
penny under your pillow. The next morning, to your surprise, you find two pennies under your pillow. The following morning, you find four pennies, and the morning after
that, eight pennies.
Suppose that you could keep making a single stack of the pennies. After how many days would the stack be long enough to reach a star that is about 3x10¹3 km
away? (Assume that 1 penny = 1.5 mm)

Sagot :

oladayoademosu

The number of  days would the stack be long enough to reach a star that is about 3 × 10¹³ km away is 64 days

How to find the number of days the penny would stack?

Since from the question, we see that the number of pennies double with each day. It forms a geoemetric progression with

  • first term a = L and
  • common ratio , r = 2.

Since the number of pennies after n days equals N = 2ⁿ

Let

  • L = length of 1 penny = 1.5 mm = 1.5 × 10⁻³ m

So, after n days, the length of the stack of pennies is the geoemetric progression D = 2ⁿ × L

Number of days pennies would stack to reach star

Making n subject of the formula, we have

n = ㏒(D/L)/㏒2

  • Since D = the distance of the star = 3 × 10¹³ km = 3 × 10¹⁶ m, and
  • L = length of 1 penny = 1.5 mm = 1.5 × 10⁻³ m

Substituting the values of the variables into the equation, we have

n = ㏒(D/L)/㏒2

n = ㏒(3 × 10¹⁶ m/1.5 × 10⁻³ m)/㏒2

n = ㏒(3/1.5 × 10¹⁹)/㏒2

n = ㏒(2 × 10¹⁹)/㏒2

n = ㏒2 + ㏒10¹⁹/㏒2

n = (19㏒10 + ㏒2)/㏒2

n = (19 + 0.3010)/0.3010

n = 19.3010/0.3010

n = 64.1

n ≅ 64 days

So, the number of  days would the stack be long enough to reach a star that is about 3 × 10¹³ km away is 64 days

Learn more about geometric progression here:

https://brainly.com/question/26147891

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