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The growth of a colony of bacteria is given by the equation, Q = Q, e0.195t If there are initially 500 bacteria present and t is given in hours determine how many bacteria are there after a half of a day as well as how long it will take to reach a bacteria population of 10,000 in the colony.

User Mivra
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The growth of a colony of bacteria is given by the equation:

Q = Q₀ * e^(0.195t)

where:

Q₀ = initial number of bacteria

t = time in hours

Q = number of bacteria at time t

Let's calculate the number of bacteria after half a day, which is 12 hours:

Q = 500 * e^(0.195 * 12)

Using a calculator, we can evaluate this expression:

Q ≈ 500 * e^(2.34)

Q ≈ 500 * 10.397

Q ≈ 5198.5

So, after half a day (12 hours), there are approximately 5198.5 bacteria in the colony.

Next, let's determine how long it will take to reach a bacteria population of 10,000 in the colony:

Q = 10000

500 * e^(0.195t) = 10000

Dividing both sides by 500:

e^(0.195t) = 10000 / 500

e^(0.195t) = 20

Taking the natural logarithm (ln) of both sides:

0.195t = ln(20)

Now, we solve for t:

t = ln(20) / 0.195

Using a calculator:

t ≈ 6.207

So, it will take approximately 6.207 hours to reach a bacteria population of 10,000 in the colony.

User Vazid
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