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Eduardwww [97]
3 years ago
12

A bacteria colony increases in size at a rate of 4.0581e1.6t bacteria per hour. If the initial population is 36 bacteria, find t

he population four hours later. (Round your answer to the nearest whole number.)
Mathematics
1 answer:
Harrizon [31]3 years ago
3 0

Answer:

1560

Step-by-step explanation:

The rate of Increase of the population (P) of the bacteria is given as:

\frac{dP}{dt} =4.058e^{1.6t}

dP =4.058e^{1.6t}}dt\\Taking\: Integrals\\\int dP =4.058 \int e^{1.6t}dt\\P(t)=\frac{4.058}{1.6} (e^{1.6t} +K)\\P(t)=2.53625 (e^{1.6t} +K)

Where k is a constant of Integration.

At t=0, P(t)=36

36=2.53625 (e^{1.6*0} +K)\\36=2.53625 (e^{0} +K)\\36=2.53625 (1 +K)\\36=2.53625 +2.53625K\\K=13.19

Therefore:

P(t)=2.53625 (e^{1.6t} +13.19)\\At \: t=4\\P(4)=2.53625 (e^{1.6*4} +13.19)\\=1559.88\\P(4)=1560

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There are two numbers
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I take it there are two such numbers.
Let one number = x
Let one number = y

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Put equation 1 into equation 2
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\text{x = }\dfrac{ -0.5 \pm \sqrt{0.5^{2} - 4*1*1 } }{2*1}

x = [-0.5 +/- sqrt(0.25 - 4)] / 2
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x1 = -0.25 + 0.9682 i
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The complex parts cancel out.  Getting them to multiply to 1 will be a little more difficult. I'll do that under the check.

Check
(-0.25 - 0.9682i)(-0.25 + 0.9682i)
Use FOIL
F:-0.25 * -0.25 = 0.0625
O: -0.25*0.9682i
I: +0.25*0.9682i
L: -0.9682i*0.9682i = - 0.9375 i^2 = 0.9375

Notice
The two middle terms (labled "O" and "I" ) cancel out. They are of opposite signs.

The final result is 0.9375 and 0.0625 add up to 1
 
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