Question14
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The function gives the number of bacteria in a population minutes after an initial observation. How much time, in minutes, does it take for the number of bacteria in the population to double?
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Studdy Solution
STEP 1
1. The function represents the number of bacteria at time minutes.
2. We need to find the time when the number of bacteria doubles from its initial amount.
STEP 2
1. Determine the initial number of bacteria.
2. Set up an equation for the doubled bacteria count.
3. Solve the equation for .
STEP 3
Determine the initial number of bacteria.
The initial number of bacteria is given by .
STEP 4
Set up an equation for the doubled bacteria count.
The bacteria count doubles when it reaches .
Set .
STEP 5
Solve the equation for .
Divide both sides by 60,000 to isolate the exponential term:
Since , we have:
Multiply both sides by 40 to solve for :
It takes minutes for the number of bacteria to double.
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