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ELEN [110]
2 years ago
12

Suppose the bacteria population in a specimen increases at a rate proportional to the population at each moment. There were 100

bacteria 4 days ago and 100,000 bacteria 2 days ago. How many bacteria will there be by tomorrow
Mathematics
1 answer:
NNADVOKAT [17]2 years ago
7 0

9514 1404 393

Answer:

  about 3,160,000,000

Step-by-step explanation:

"Increases at a rate proportional to population" means the growth is exponential. It can be modeled by the equation ...

  p = ab^t

We can find 'a' and 'b' using the given data points.

  100 = ab^(-4) . . . . . . . population 4 days ago

  100,000 = ab^(-2) . . . population 2 days ago

Dividing the second equation by the first, we find ...

  1000 = b^2

  b = 1000^(1/2)

Substituting for b in the first equation, we have ...

  100 = a(1000^(1/2))^(-4) = a(1000^-2)

  100,000,000 = a

Then the population model is ...

  p = 100,000,000×1000^(t/2)

__

Tomorrow (t=1), the population will be ...

  p = 100,000,000 × 1000^(1/2) ≈ 31.6 × 100,000,000

  p ≈ 3,160,000,000 . . . . . bacteria by tomorrow

_____

<em>Additional comment</em>

We could write this as ...

  p = 10^(8+1.5t)

Then for t=1, this is p = 10^(8+1.5) = 10^0.5 × 10^9 = 3.16×10^9

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2 years ago
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Answer:

Table shown below

Step-by-step explanation:

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3 years ago
Solve for b.
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3 0
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On a biased dice the probability of getting 1 is 0.3. The ice is rolled 150 times. How many ones would you expect to roll?
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Answer:  45

=====================================================

Work Shown:

n = number of rolls = 150

p = probability of rolling a "1" = 0.3

n*p = expected number of "1"s that show up out of the 150 rolls

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