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SpyIntel [72]
3 years ago
10

There are 70,000 bacteria present in a culture. An antibiotic is introduced to the culture and the number of bacteria is reduced

by half every 4 hours. Which of the following statements are true? Select all that apply

Mathematics
1 answer:
Harlamova29_29 [7]3 years ago
6 0

Answer:

24 hours after the antibiotic is introduced, the number of bacteria in the culture is reduced to 1093; The amount of bacteria present in the culture during the 24 hours after the antibiotic is introduced is an example of exponential decay; The function B(x) = 70000(0.5)ˣ, where x represents the number of 4 hour periods, represents the amount of bacteria present after the antibiotic is introduced.

Step-by-step explanation:

In any situation where an amount grows or declines by a set percent every time period can be represented using an exponential function.  Since the amount of bacteria is reduced by half, or 50%, every 4 hours, this is exponential decay.

Exponential functions such as this are of the form

y = a(1+r)ˣ, where a represents the initial population, r is the percent of growth or decrease, and x is the number of time periods.  In this situation, the initial population, a, is 70000.  Since the number of bacteria decreases by half, r = -0.50.  This gives us

y = 70000(1+-0.50)ˣ, or y = 70000(0.50)ˣ.

In 24 hours, there are 6 4-hour periods.  This means x = 6; this gives us

y = 70000(0.50)⁶ = 1093.75.

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Bezzdna [24]
Refer to the diagram shown below.

The velocity of the person on the walkway relative to the ground is the velocity of the walkway (relative to the ground) plus the velocity of the person relative to the walkway.
It is
1.0 + 0.5 = 1.5 m/s

The person on the ground moves at - 0.2 m/s, which is in the opposite direction to that of the walkway and the person on the walkway.
Therefore the velocity of the person on the walkway relative to the person on the ground is
105 - (-0.2) = 1.7 m/s

Answer: 1.7 m/s

7 0
3 years ago
Answer all questions, your combing like terms. Show ALL of you work! Thank you!!
Elanso [62]

Answer:

1. -12x - 9y - 6

2. -12x + 36

3. -240

4. -2

5. x = -57

6. x = -6

7. x = 48

8. x = 20

9. x = -288

10. n = 8

Step-by-step explanation:

1.

-5x - 13 + 3y - 7x - 12y + 7

-12x - 13 + 3y - 12y +  7

-12x - 6 + 3y - 12y

-12x - 6 - 9y

-12x - 9y - 6

2.

-3(4x - 12)

-3(4x) + (-3)(-12)

-12x + 36

3.

6x - 282

6(7) - 282

42 - 282

-240

4.

6x + 2(y + x)

6(-2) + 2(7 + (-2))

-12 + 2(7 - 2)

-12 + 2(5)

-12 + 10

-2

5.

x - 23 = -80

 + 23    +23

x = -57  

6.

12x = -72

/12     /12

x = -6

7.

x/4 = 12

* 4    * 4

x = 48

8.

3x + 12 = 72

    -  12  - 12

3x = 60

/3     /3

x = 20

9.

x/4 - 8 = -80

     + 8    + 8

x/4 = -72

* 4    * 4

x = -288

10.

-4(1 - 5n) - 8n = 92

-4 + (-4)(-5n) - 8n = 92

-4 + 20n - 8n = 92

-4 + 12n = 92

12n - 4 = 92

     + 4    + 4

12n = 96

/12     /12

n = 8

6 0
2 years ago
100 points
Snezhnost [94]

Answer: 28\sqrt 3

Step-by-step explanation:

8 x 14 x 21 = 2352, so:

√8⋅√14⋅√21 = √2352

√2352 in simplest form is 28√3

I hope this helps!

6 0
2 years ago
20 less than a number
agasfer [191]

Answer:

20 less than a number is equal to the number.

Step-by-step explanation:

8 0
2 years ago
(2)/(7):0.6x=(4)/(21):0.25
inysia [295]

Answer:

 =  1.6

Unless you meant to clarify what in the equation you needed, but that is the answer to it.

7 0
2 years ago
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