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irga5000 [103]
2 years ago
7

="TexFormula1" title=" (-5g^{5}h^{6})^{2}(g^{4}h^{2})^4 " alt=" (-5g^{5}h^{6})^{2}(g^{4}h^{2})^4 " align="absmiddle" class="latex-formula">
Mathematics
1 answer:
Elenna [48]2 years ago
3 0
I dont understand this
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The population of bacteria in a culture grows at a rate proportional to the number of bacteria present at time t. After 3 hours
Arada [10]

Answer:

The number of bacteria at initial = 187

Step-by-step explanation:

Given that the population of bacteria in a culture grows at a rate proportional to the number of bacteria present at time t.

\frac{dN}{dt} = k N

\frac{dN}{N}  = k dt

Integrating both side we get

㏑ N = k t + C ------- (1)

Now given that after 3 hours it is observed that 500 bacteria are present and after 10 hours 5000 bacteria are present.

⇒ ㏑ 500 = 3 k + C -------- (2)

⇒ ㏑ 5000 = 10 k + C ------ (3)

⇒ ㏑ 5000 -  ㏑ 500 = 7 k

⇒ ㏑\frac{5000}{500} = 7 k

⇒  ㏑ 10 = 7 k

⇒ k = 0.329

Put this value of k in equation (2),

⇒ ㏑ 500 = 3 × 0.329 + C

⇒ C = 5.23

Put this value of C in equation 1 we get,

⇒ ㏑ N = k t + 5.23

Initially when t = 0 , then

⇒ ㏑ N = 5.23

⇒ N =  187

Thus the number of bacteria at initial = 187

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3 years ago
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Step-by-step explanation:

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