MATHEMATICS MIDDLE SCHOOL

The population P of a bacteria culture is modeled by P = 4100e^kt where t is the time inhours. If the population of the culture was 5800 after 40 hours, how long does it take for
the population to double? Round to the nearest tenth of an hour.

Show work please
A LOT OF POINTS

Answers

Answer 1
Answer:

Enter the given values into the equation and solve.

5800 = 4100e^(k*40)

Divide both sides by 4100 and simplify:

58 / 41 = e^(k*40)

Remove e by taking the logarithm of both sides:

ln(58/41) = k *40

Divide both sides by 40:

k = ln(58/41)/40

k = 0.00867

Now for the population to double set up the equation:

2*4100 = 4100e^kt

The 4100 cancels out on both sides:

2 = e^kt

Take the logarithm of both sides:

ln(2) = k*t

Divide both sides by k

t = ln(2) /k

replace k with the value from above:

t = ln(2) / 0.00867

t = 79.95

Rounded to the nearest tenth = 80.0 hours to double.
Answer 2
Answer:

Answer:

It would take around 122 hours to double the population.

Step-by-step explanation:

To answer the question, we first need to find the constant k, using the given information and the expression.

P=4100e^(kt) \n5800=4100e^(k(40)) \n(5800)/(4100)=e^(40k)\ne^(40k)=1.41\nlne^(40k)=ln1.41\n40k=0.34\nk=(0.34)/(40)\approx 0.0085

Now that we have the constant. We can find the time it would take to double the population which would be 11600:

P=4100e^(kt)\n11600=4100e^(0.0085t)\n(11600)/(4100)= e^(0.0085t)\ne^(0.0085t)=2.83\nlne^(0.0085t)=ln2.83\n0.0085t=1.04\nt=(1.04)/(0.0085)\approx 122.35

Therefore, it would take around 122 hours to double the population.

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Answers

the answer is the first one. p>-2 and p<5. you must choose the first one because the circle is uncoloured

Answer:

Step-by-step explanation:

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Does anyone know what this equation is?96i+245=53
I just need to know what the variable is.

Answers

Answer:

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Step-by-step explanation:

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i is the variable hope this helps

Convert the following fractions to decim 30/20

Answers

For this case we must convert the following fraction into a decimal number:

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Answer:

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Answer:

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Answers

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Answers

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Hope that helped :) 
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Answers

-4x + 7 = 11 

First, subtract 7 from both sides. / Your problem should look like: -4x = 11 - 7
Second, subtract 11 - 7. / Your problem should look like: -4x = 4
Third, divide both sides by -4. / Your problem should look like: x = (4)/(-4)
Fourth, change the fraction to a negative. / Your problem should look like: x = -(4)/(4)
Fifth, cancel 4 out. / Your problem should look like: x = -1

Answer: x = -1
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-4x=4           (divide -4 on both sides)
x=-1
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