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# Interpret change in exponential models: with manipulation

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## Problem

After a special medicine is introduced into a petri dish full of bacteria, the number of bacteria remaining in the dish decreases rapidly.
The relationship between the elapsed time t, in seconds, and the number of bacteria, B, left parenthesis, t, right parenthesis, in the petri dish is modeled by the following function:

### $B(t)=9300\cdot \left(\dfrac{1}{64}\right)^{t}$B, left parenthesis, t, right parenthesis, equals, 9300, dot, left parenthesis, start fraction, 1, divided by, 64, end fraction, right parenthesis, start superscript, t, end superscript

Complete the following sentence about the rate of change of the bacterial culture. Round your answer to two decimal places.
The bacterial culture loses start fraction, 1, divided by, 2, end fraction of its size every
seconds.
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