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Sergio [31]
3 years ago
11

During the exponential phase, E. coli bacteria in a culture increase in number at a rate proportional to the current population.

If the growth rate is 1.9% per minute and the current population is 172.0 million, what will the population be 7.2 minutes from now?
Mathematics
1 answer:
NikAS [45]3 years ago
8 0

Answer:

  197.2 million

Step-by-step explanation:

The appropriate exponential equation for the population is ...

  p(t) = 172.0e^(0.019t)

Then we can compute for t=7.2:

  p(7.2) = 172.0e^(0.019·7.2) ≈ 172.0·1.146599 ≈ 197.2

7.2 minutes from now, the population will be about 197.2 million.

___

For continuous growth (or continuous compounding), the exponential formula is ...

  f(t) = (value at t=0)×e^(rt)

where r is the growth rate in one unit of time, and t is the number of time periods.

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Answer:

4. 50,000 square miles

5. The office would round to $800,000 instead of $700,000 because they would lose that needed $35,495. If they rounded down, their budget would be cut short, and they won’t have enough money for the office.

6. Five numbers that could also be the population: 577,777; 575,555; 578,999: 578,787; 581,545.

7. 600,000

8.584,000

9. 260,000

Step-by-step explanation:

4. In this question, we’re rounding the number, “54,555” go the nearest ten thousand. When rounding numbers you look at the number next to the digit your rounding. In this case, since the second number is not 5 or higher, we round it to 50,000 as that’s closer than 60,000.

5. Like I stated above: if they round to the lowest amount, they won’t have enough money to but what they need. Therefore, even if according to rounding it needs to be lower, it will not be beneficial to the company.

6. This are all possible numbers cause they can all by round to 580,000 AND 600,000

7. Since the number next to six is not five or higher, we round it to the closest number which is 600,000.

8. Since the number next to 3 is 5, we round it to the higher number. So it’s 584,000

9. Since the number next to the underlined nunber is 6, we round it to the closest number which is 260,000

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3 years ago
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Answer:

∠ EFG = 83°, ∠ GCE = 97°

Step-by-step explanation:

Since FE and FG are tangents to the circle then

∠ FGC and ∠ FEC are right angles

The sum of the angles in quadrilateral CEFG = 360°

Sum the 4 angles and equate to 360

3x + 11 + 90 + 5x - 23 + 90 = 360, that is

8x + 168 = 360 ( subtract 168 from both sides )

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∠ GCE = 5x - 23 = 5(24) - 23 = 120 - 23 = 97°

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