20 ft = how many yards and how many feet?
2 answers:
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The movement of the ping pong ball follows a exponential progression.
- The expression for the k-th bounce is:
- The height after the 6th bounce is 41.82 ft
- The total distance after the 12th bounce is 1584.84ft.
- There will be 31457280 bacteria after a day and a half.
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<u>1. Ping pong ball</u>
The given parameters are:
--- the initial height
--- the common ratio
<u>(a) The expression after bouncing k times</u>
To do this, we make use of
So, we have:
In this case; k = n.
So, the equation becomes
Hence, the expression for the k-th bounce is:
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<u>(b) The height after bouncing 6 times</u>
This means that k = 6.
So, we have:
Hence, the height after the 6th bounce is 41.82 ft
<u>(c) The total distance after the 12th bounce</u>
First, we calculate the total height after the 12th bounce using:
So, we have:
So, the total distance is:
Hence, the total distance after the 12th bounce is 1584.84ft.
<u>(2) Cell division</u>
The given parameters are:
<em /><em> --- rate</em>
<em /><em> --- initial number of cells</em>
<em /><em> --- number of 2 hours is a day and a half</em>
<em />
So, the number of bacteria is:
This gives
Hence, there will be 31457280 bacteria after a day and a half.
Read more about exponential functions at: