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nadezda [96]
3 years ago
8

A freshly inoculated bacterial culture of Streptococcus contains 100 cells. When the culture is checked 60 minutes later, it is

determined that there are 450 cells present. Assuming exponential growth, determine the number of cells present at any time t (measured in minutes) and the find the doubling time.​
Mathematics
1 answer:
Luba_88 [7]3 years ago
7 0

Answer:

P(t) = 100e^{0.0251t}

The doubling time is of 27.65 minutes.

Step-by-step explanation:

Exponential equation of growth:

The exponential equation for population growth is given by:

P(t) = P(0)e^{kt}

In which P(0) is the initial value and k is the growth rate.

A freshly inoculated bacterial culture of Streptococcus contains 100 cells.

This means that P(0) = 100. So

P(t) = 100e^{kt}

When the culture is checked 60 minutes later, it is determined that there are 450 cells present.

This means that P(60) = 450, and we use this to find k. So

450 = 100e^{60k}

e^{60k} = 4.5

\ln{e^{60k}} = \ln{4.5}

60k = \ln{4.5}

k = \frac{\ln{4.5}}{60}

k = 0.0251

So

P(t) = 100e^{0.0251t}

Doubling time:

This is t for which P(t) = 2P(0) = 200. So

200 = 100e^{0.0251t}

e^{0.0251t} = 2

\ln{e^{0.0251t}} = \ln{2}

0.0251t = \ln{2}

t = \frac{\ln{2}}{0.0251}

t = 27.65

The doubling time is of 27.65 minutes.

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Answer:

a) 1,360,760,000

b) 1,361,000,000

c) 1,400,000,000

d)  1,360,800,000

Step-by-step explanation:

We have to round off the given population number to certain digits.

The following are the rules to round of a number:

  1. First identify the digit to be rounded.
  2. If this digit is followed by 5,6,7,8,9 then we round up the number that is increase the digit by 1 and all the numbers to right becomes zero.
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a)  to the nearest thousand.

Thousands place: 0

Right Digit: 1

We round down the number

Rounded to the nearest 1,000 or t he thousands Place =  1,360,760,000

b)  to the nearest million

Millions place: 0

Right Digit: 7

We round up the number

Rounded to the nearest million places = 1,361,000,000

c)  to nearest hundred million

Hundred million place: 3

Right Digit: 6

We round up the number

Rounded to the nearest million places = 1,400,000,000

d)  to the nearest hundred thousand.

hundred thousand place: 7

Right Digit: 6

We round up the number

Rounded to the nearest million places = 1,360,800,000

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Answer:

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Step-by-step explanation:

a dozen is 12. So 5 times 12 is 60.

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Bob drove at an average speed of 15km/h correct to the nearest unit. He drove for 3 hours, correct to the nearest hour. What is
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Answer:

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Step-by-step explanation:

Given data

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I'm pretty sure the answer is
<span>B. y = 6x
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