Question 1027007: A penny is 1.55 mm thick. Imagine that you stack pennies on top of each other every day. Each day, you double the amount of pennies in the stack. This means that on day 0, there is 1 penny. On day 1, there are 2 pennies. On day 2, there are 4 pennies, etc.
If this pattern continues, in how many days will the stack of pennies be about 1 meter tall?
Also, the distance from the earth to the moon is 405,696,000 meters. About how many stacked
pennies would it take to reach the moon? Round to the nearest hundredth. After about how many days will the stack of pennies be tall enough to reach the moon?
Thanks!
Answer by mathmate(429)   (Show Source):
You can put this solution on YOUR website!
Question:
A penny is 1.55 mm thick. Imagine that you stack pennies on top of each other every day. Each day, you double the amount of pennies in the stack. This means that on day 0, there is 1 penny. On day 1, there are 2 pennies. On day 2, there are 4 pennies, etc.
If this pattern continues, in how many days will the stack of pennies be about 1 meter tall?
Also, the distance from the earth to the moon is 405,696,000 meters. About how many stacked
pennies would it take to reach the moon? Round to the nearest hundredth. After about how many days will the stack of pennies be tall enough to reach the moon?
Solution:
This is not an easy question because the accuracy of the answer required needs around 14 digits of accuracy, which is beyond most calculators.
Anyway, let's get going.
The distance to the moon is given as 405,696,000 meters.
Each penny is 1.55 mm thick.
The number of pennies required will therefore be
405,696,000 metres * (1000 mm/metre) / 1.55 mm
= 261739354838.70966992
= 261739354838.71 (to two decimal places)
To see how many days it takes, we see that
day 0: 1= penny
day 1: 2= pennies
day 2: 4= pennies
...
day n:  pennies.
So we are left with solving the following equation for n :
261739354838.70966992 =
taking log on both sides,
n*log(2) = 
or
n= 
=37.9293399 (approximately) days
I will leave it to you to do the first part (how many pennies in 1 metre, or 1000 mm), which can be handled using a regular calculator.
Interesting facts about moon-earth distance (measured centre to centre):
The distance of the earth to the moon varies daily.
Today the distance is approximately 397,480,164 metres at 07:28:28 EST.
The distance varies from 356,500 km (221,500 mi) at the perigee to 406,700 km (252,700 mi) at apogee,
It equals approximately 1/400 of the distance from the earth to the sun (1 AU).
The earth-moon distance could vary by up to 75 m/s!
It takes about 37 seconds for light to travel from the moon to earth.
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