SOLUTION: A scientist notes the bacteria count in a petrie dish is 50. Two hours later, he notes the count has increased to 80. If this rate of growth continues, how much more time will it t

Question 133251: A scientist notes the bacteria count in a petrie dish is 50. Two hours later, he notes the count has increased to 80. If this rate of growth continues, how much more time will it take for the bacteria count to reach 100?
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
A scientist notes the bacteria count in a petrie dish is 50. Two hours later, he notes the count has increased to 80. If this rate of growth continues, how much more time will it take for the bacteria count to reach 100?
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count = a*b^x
You have two points: (0,50) and (2,80)
50 = a*b^0
a = 50
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So, count = 50*b^x
8/5 = b^2
Take the square root to get:
b = sqrt(8/5)
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Growth Equation:
count = 50*(sqrt(8/5))^x
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Let the count be 100; solve for "x":
100 = 50*(sqrt(8/5))^x
(sqrt(8/5))^x = 2
x log(sqrt(8/5)) = log2
x = log2/[log(sqrt(8/5))
x = 2.949539695..... hours
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Cheers,
Stan H.
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