Question 1096132: A. A penny is 1.55 mm thick. About how many pennies can you stack on top of each other in order to get one meter? Round to the nearest hundredth.(Hint: There are 1000 mm in meter).
B. 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. What exponential function is being modeled here?
C. If this pattern continues, in how many days will the stack of pennies be about 1 meter tall?
D. 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.
E. After about how many days will the stack of pennies be tall enough to reach the moon?
I know answer A is 645 pennies = 1 meter,
C is n= number of days N=2n.
645.378*00155 = 1.00034
can someone help me with questions B,D,and E please?
Answer by Boreal(15235)   (Show Source):
You can put this solution on YOUR website! that is a geometric series of 2^0, 2^1, 2^2, ..., and the sum of h terms is 2^h-1, with the common ratio 2.
1000/1.55=645.16 pennies
645.16=2^h-1
646.16=2^h
take ln both sides
ln (646.16)=h ln 2
h=ln 646.16/ln 2
9.33 days (1,2,4,8,16,32,64,128,256, and on the 10th day it will reach and pass 1 meter.
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405,696,000 meters * 645.16 pennies/meter=2.617 x 10^11 pennies.
This is 261,738,831,400
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261,738,831,400=2^h-1
can ignore the 1
ln both sides
26.2906=h ln 2
h=37.93 days (on the 38th day)
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