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Ulleksa [173]
3 years ago
9

A bacteria culture initially contains 100 cells and grows at a rate proportional to its size. After an hour the population has i

ncreased to 230. (a) Find an expression for the number of bacteria after t hours. (b) Find the number of bacteria after 2 hours. (Round your answer to the nearest whole number.) P(2) = ___bacteria (c) Find the rate of growth after 2 hours. (Round your answer to the nearest whole number.) P'(2) = ___bacteria per hour (d) When will the population reach 10,000? (Round your answer to one decimal place.) t = ___hr

Mathematics
1 answer:
goldfiish [28.3K]3 years ago
6 0

Answer:

  • P(t) = 100·2.3^t
  • 529 after 2 hours
  • 441 per hour, rate of growth at 2 hours
  • 5.5 hours to reach 10,000

Step-by-step explanation:

It often works well to write an exponential expression as ...

   value = (initial value)×(growth factor)^(t/(growth period))

(a) Here, the growth factor for the bacteria is given as 230/100 = 2.3 in a period of 1 hour. The initial number is 100, so we can write the pupulation function as ...

  P(t) = 100·2.3^t

__

(b) P(2) = 100·2.3^2 = 529 . . . number after 2 hours

__

(c) P'(t) = ln(2.3)P(t) ≈ 83.2909·2.3^t

  P'(2) = 83.2909·2.3^2 ≈ 441 . . . bacteria per hour

__

(d) We want to find t such that ...

  P(t) = 10000

  100·2.3^t = 10000 . . . substitute for P(t)

  2.3^t = 100 . . . . . . . . divide by 100

  t·log(2.3) = log(100)

  t = 2/log(2.3) ≈ 5.5 . . . hours until the population reaches 10,000

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NeTakaya

Answer:

She caught 10 rabbits

Step-by-step explanation:

Given

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S = 3D

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S + R+ D = 10 +4D

Required

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S + R+ D = 10 +4D

Solve for R

R = 10 + 4D - D - S

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8 0
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A survey showed that 35% of the students prefer plain white milk over chocolate milk. If the school has 1200 students. How many
Pani-rosa [81]

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Step-by-step explanation:

Let,

the total percentage = 100%

Students who prefer plain white milk = 35%

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No. of students who prefer chocolate milk = 65% of total students

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No. of students who prefer chocolate milk = \frac{78000}{100}\\

No. of students who prefer chocolate milk = 780

780 students prefer chocolate milk.

Keywords: percentage, subtraction

Learn more about subtraction at:

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Step-by-step explanation:

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7 0
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