SOLUTION: Solve the problem. Please show your work.
1. The population of a colony of bacteria is decaying exponentially according to the function below, where t is the time in minutes. Ho
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Question 214806: Solve the problem. Please show your work.
1. The population of a colony of bacteria is decaying exponentially according to the function below, where t is the time in minutes. How many minutes will it take for the population of the colony to drop to 50?
B(t)=2000*e^(-.03*t)
e=2.718
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
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Substitute 50 for B(t) to get:
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Take the natural log of both sides to get:
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rules of logarithms apply here.
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first rule:
second rule:
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applying the first rule,
becomes
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applying the second rule,
becomes
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putting this all together, your equation becomes:
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equals 1, so your equation becomes:
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subtract ln(2000) from both sides of this equation and then divide both sides of this equation by (-.03) to get:
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this becomes:
this becomes:
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The population will decay to 50 in 122.9626485 hours.
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substitute this value for t in the original equation to get:
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this becomes:
confirming that is a good value for t.
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