SOLUTION: 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

Algebra ->  Exponential-and-logarithmic-functions -> SOLUTION: 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       Log On


   

Question 1027006: 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? If this pattern continues, in how many days will the stack of pennies be about 1 meter tall? BTW the pennies are 1.55 mm's thick
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +N+ = number of pennies after +n+ days
+N+=+2%5En+
The thickness of the stack in meters would be:
+.00155N+
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In how many days will the stack of pennies be about 1 meter tall?
+N+=+2%5En+
The thickness of the stack in meters =
+.00155%2A2%5En+
+1+=+.00155%2A2%5En+
+2%5En+=+1%2F.00155+
+2%5En+=+645.16+
I can take the log of both sides
+n%2Alog%282%29+=+log%28+645.16+%29+
+.301n+=+2.81+
+n+=+9.334+
In 9 days the stack will be 1 meter tall
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check:
+N+=+2%5En+
+N+=+2%5E9.334+
+N+=+645.378+
+645.378%2A.00155+=+1.00034+
close enough