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.
A.) two hours after the antibody is introduced , there are 35000 bacteria present in the culture
B.) 24 hours after the antibiotic is introduced , the number if bacteria in the culture is reduced to 1093
C.) the number of present in the culture during the 24 hours after the the antibiotic is introduced is an example of exponential decay
D.) the half-life of the bacteria after the antibiotic is introduced is 2 hours
E.)the function B(x)=70000(0.5)^x where x is the number of 4 hour periods represents the amount of bacteria present after the antibiotic is introduced

Answers

Answer 1

Answer:

c

Step-by-step explanation:

the number of bacteria is introduced

Answer 2

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. Therefore, option D is the correct answer.

What is the exponential function?

Exponential function, as its name suggests, involves exponents. But note that, an exponential function has a constant as its base and a variable as its exponent but not the other way round (if a function has a variable as the base and a constant as the exponent then it is a power function but not an exponential function).

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.

Therefore, option D is the correct answer.

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Related Questions

graph the circle x^2+y^2+2x+4y-44=0

Answers

plot the circle on a coordinate plane, with the center at (-1, -2) and a radius of 7 units.

To graph the equation of the circle x^2 + y^2 + 2x + 4y - 44 = 0, we can follow these steps:

1. Complete the square for the x-terms:

  Rearrange the equation to group the x-terms together:

  x^2 + 2x + y^2 + 4y = 44

  To complete the square for the x-terms, add (2/2)^2 = 1 to both sides of the equation:

  x^2 + 2x + 1 + y^2 + 4y = 44 + 1

  Simplify:

  (x + 1)^2 + y^2 + 4y = 45

2. Complete the square for the y-terms:

  To complete the square for the y-terms, add (4/2)^2 = 4 to both sides of the equation:

  (x + 1)^2 + y^2 + 4y + 4 = 45 + 4

  Simplify:

  (x + 1)^2 + (y + 2)^2 = 49

3. Identify the center and radius:

  The equation is now in the standard form of a circle: (x - h)^2 + (y - k)^2 = r^2

  Comparing this with our equation, we can see that the center of the circle is (-1, -2) and the radius is √49 = 7.

4. Plot the graph:

  The center of the circle is (-1, -2), which represents the point where the circle is centered. From this point, we can draw a circle with a radius of 7 units in all directions.

By following these steps, we can plot the circle on a coordinate plane, with the center at (-1, -2) and a radius of 7 units.

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Note the full question may be:

To graph the equation of the circle x^2 + y^2 + 2x + 4y - 44 = 0, first rewrite it in standard form by completing the square for both x and y terms. Then identify the center and radius of the circle and plot the corresponding points to draw the graph.

Explain the three steps when using distributive property to write an equivalent expression.

Answers

Answer:

Step-by-step explanation:First you apply the distributive property to create equivalent expressions, then you use algebra tiles to write equivalent expressions, and finally you verify that two different values of the variable yield the same value for each expressions, then the expressions are equivalent .

Please help me now plz I will mark you brainliest

Answers

Answer:

On the circle

Step-by-step explanation:

Because all of the points on a circle are equidistant from the center, if a circle has a radius of 10 then all of the points are 10 units from the center. Using the Pythagorean Theorem, you know that the distance from (4,0) to (-2,8) is:

[tex]\sqrt{(4-(-2))^2+(8-0)^2}=\sqrt{6^2+8^2}=\sqrt{36+64}=\sqrt{100}=10[/tex], meaning that it is on the circle. Hope this helps!

The base of a rectangular prism has an area of 252525 square meters. The height of the rectangular prism is 444 meters. What is the volume, in cubic meters, of this rectangular prism?

Answers

Answer:Height:  

15.8  meters

Explanation: For a rectangular prism:  XXX  Volume  =  height  ×  width  ×  depth  and  XXX  Area (of base)  =  width  ×  depth  ⇒  height  =  Volume  Area  =  306.52

19.4  =  15.

Answer:  100 CUBIC METERS

Step-by-step explanation:

triangle xyz is similar to triangle abc solve for k

Answers

Answer:

k = 13.5

Step-by-step explanation:

We can use ratios to solve

3        4.5

---- = ---------

9          k

Using cross products

3k = 9*4/5

Divide each side by 3

3k/3 = 9*4.5/3

k =13.5

The correct answer is 13.5

A square pyramid is sliced parallel to the base and halfway up the pyramid.
Which of these describes the cross section?

A square smaller than the base
A quadrilateral that is not a square
A square the same size as the base
A triangle with a height the same as the pyramid

Answers

Answer:

A square smaller than the base

Explanation:

A square pyramid is a 3 Dimensional image. When you slice a 3 Dimensional image you form is a 2 Dimensional image for example a rectangle, a square, a triangle e.t.c.

The shape of the cross sections formed after slicing a 3 Dimensional image is dependent on the way it was sliced.

This means it can be sliced horizontally or vertically and this would result in different shapes.

If square pyramid is sliced parallel to the base and halfway up the pyramid, the shape of the cross section formed is a square smaller than the base.

Answer:

the first one

Step-by-step explanation:

what is the circumference of a circle with the radius of 7 units

Answers

Answer:

43.98

Step-by-step explanation:

What's the mean of 3 4 5 3 4 5 6 7 1 2 3 4 5 6 4 8 4 3 2
A. 4.1
B.4.2
C.8.0
D.8.3

Answers

Answer:

A. 4.1

Step-by-step explanation:

3+4+ 5+ 3+ 4+ 5+ 6+ 7+ 1+ 2+ 3+ 4+ 5+ 6+ 4+ 8+ 4+ 3+ 2= 79

79/ 19 = 4.1

A bag of Super dog food, at $12.85, is one third the price of a bag of power dog food. Write and solve a division equation to find the price of a Power Dog dog food.

Answers

Answer:

4.283

Step-by-step explanation:

Divide 12.85 by 3 using a calculator

Julie has four times as many pairs of shoes as her brother. Together they have 15 pairs of shoes. How many pairs of shoes do they each have?

Answers

Answer:

60 pairs of shoes

Step-by-step explanation:

To find the answer, multiply 4x15. The words four times as many mean to do the operation of multiplication. 4x15= 60 So finally, each have 60 pairs of shoes.

i hope this helped:)

Answer:

7.5

Step-by-step:

Julie: ?

Her brother: ?

Total number: 15

So: 15 divided to julie and her brother-

There for 15 divide by 2 is 7.5

7.5+7.5=15

Write the standard equation for a circle with center (0,0) and radius 8

Answers

Answer:

Step-by-step explanation:

hello : an equation is :

x²+y²=64

Please need this by the 16th

Answers

Answer:

60

Step-by-step explanation:

12 can be broken into 3*4

15 = 5*3

The least  factors are

3*4*5 = 60

The lowest common denominator is 60

Answer:

7/12= 35/60

7/15= 28/60


Which equation is NOT an example of a linear function?
A) y = 9 - 2x
B) y = 6/X
C) y = x/2 + 9
D) y = 5/6x - 8

Answers

Answer:

B

Step-by-step explanation:

y = 6/x is not  an example of a linear function

Option B is correct

A linear function can be written in the form ax + by = c

Let us consider the options given and see which of them cannot be expressed in the form ax + by + c

For y  =   9  -  2x

This can also be expressed as

-2x + y  =  9

For y  =  x/2  +  9

This can also be expressed as:

x  -  2y  =  - 18

For y  =  5/6 x - 8

This can also be expressed as:

-5x  +  6y  =  -48

Only y = 6/x cannot be expressed in the form ax + by = c. Therefore, y  = 6/x is not an example of a linear function

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Figure A is a scale image of Figure B.
What is the value of x?

Answers

Answer:

x/2 = 12.5/5

5 · x = 12.5 · 2

5x = 25

5x / 5 = 25 / 5

x = 5

Step-by-step explanation:

Select ALL equations that have a solution of 6.

A
x + 6 = 9
3
B
4x + 15 = 29
C
x + 9 = 5
3
D
2(x + 5) = 18

Answers

None, i checked on photomath and it says none. What are we solving for??

Someone help me pleaseeee

Answers

Answer:

you have to add all the angles including 'x' which is equals to 180°.

The process is

99+49+x=180

148+x=180

x=180-148

x=32.

Explain what the similarities and difference between y=2cosx and y=2cosx-3.

Answers

Answer:

(See explanation for further details)

Step-by-step explanation:

Similarities: Both expression have the same slope for the same values of x.

Difference: The second expression is a translated form of the first function in -3 units.

A box of chocolates contains five milk chocolates and six dark chocolates. Mike randomly picks a chocolate and eat it. Then Mike randomly picks another chocolate and eats it. Determine the probability Mike eats two milk chocolates. Round to the hundredths place.

Answers

Answer: 0.182

Step-by-step explanation:

For the first selection, the probability of picking a milk chocolate bar is equal to the number of milk chocolate bars divided the total number of bars, this is:

p1 = 5/(6 + 5) = 5/11

In the second selection we have the same equation, but now we have  4 milk chocolate bars (because one is alredy taken)

p2 = 4/(4 + 6) = 4/10

the joint probability is:

P = p1*p2 = (5/11)*(4/10) = 0.182

find -2-(-.7)
help me plz :(

Answers

Answer: 5

Step-by-step explanation:

two negatives equal a positive, so if you are subtracting with two negatives it just like 7-2 if that makes sense :)

Answer:

5

Step-by-step explanation:

you have to multiply the 2 negative signs in between of 2 and 7 and then you will get a positive sign

since the 2 signs are different you will need to subtract.

so 7-2 equals 5 and you put the bigger number's sign which is positive

how do you write a ratio?

Answers

Answer:

number : number

Step-by-step explanation:

for example, 1:3

this means 1 to 3

so for every 1 banana there are 3 apples

Number:number
And that’s how you do ratio

PLEASE HELLPPP
what is : -4(3-5)+10-3(7+4)+30​

Answers

Answer:

15

Step-by-step explanation:

Use PEMDAS for this:

Parentheses

Exponents

Multiplication

Division

Addition

Subtraction

-4(3-5)+10-3(7+4)+30 ​= -4(-2)+10-3(11)+30

-4(-2)+10-3(11)+30 = 8+10-33+30

8+10-33+30 = 18-33+30

18-33+30 = -15+30

-15+30 = 15

Step 1: calculate in parentheses
-4•(-2)+10-3•11+30
Step 2: Multiply
8+10-33+30
Step 3: Calculate
=15

What are the answers on the sheet to the math paper "What did the teenage yardstick say to its parents? "

Answers

Answer:

I want to stand on my own three feet

Step-by-step explanation:

HELP PLEASE
write down a formula for the nth term of these patterns. The first term is n = 1.
14 ,23 ,32 ,41, 50 = nth term = ?????????

-4, -11, -18, -25, -32 = nth term = ???????????

Answers

Answer:

1st one= n9+5

2nd one=n×-7+3

brainly which is the distance between (-3,4) and (7,13)

Answers

Answer:

Root 181

Step-by-step explanation:

         Using distance formula, we know that the answer will be the square root of 181. Unfortunately, this is not a perfect square, and it is prime, so that number will remain the same.

Distance Formula: [tex]\sqrt{(13-4)^{2} + (7+3})^2} = \sqrt{181}[/tex]

Hope this helped!

The table shows the estimated number of bees, y, in a hive x days after a pesticide is released near the hive.

A 2-column table with 6 rows. The first column is labeled number of days with entries 0, 10, 20, 30, 40, 50. The second column is labeled estimated number of bees with entries 10,000; 7,500; 5,600; 4,200; 3,200; 2,400.
Which function best models the data?

y = 9,958(0.972)x
y = 0.972(9,958)x
y = 9,219x– 150
y = –150x + 9,219

Answers

Answer:

A.

Step-by-step explanation:

The given table is

Days     Bees

  0        10,000

 10        7,500

 20       5,600

 30       4,200

 40       3,200

 50       2,400

Where [tex]x[/tex] represents days and [tex]y[/tex] represents bees.

The exponential function that models this problem must be like

[tex]y=a(1-r)^{x}[/tex], which represenst an exponential decary, because in this case, the number of bees decays.

We nned to use one points, to find the rate of decay. We know that [tex]a=10,000[/tex], because it starts with 10,000 bees.

Let's use the points (10, 7500)

[tex]y=a(1-r)^{x}\\7500=10000(1-r)^{10}[/tex]

Solving for [tex]r[/tex], we have

[tex]\frac{7500}{10000}=(1-r)^{10} \\(1-r)^{10} =0.75[/tex]

Using logarithms, we have

[tex]ln((1-r)^{10}) =ln(0.75)\\10 \times ln(1-r)=ln(0.75)\\ln(1-r)=\frac{ln(0.75)}{10} \approx -0.03\\e^{ln(1-r)}=e^{-0.03}\\1-r =e^{-0.03}\\r=-e^{-0.03}+1 \approx 1.97[/tex]

Replacing all values in the model, we have

[tex]y=10000(1-1.97)^{x}\\y=10000(0.97)^{x}[/tex]

Therefore, the right answer is the first choice, that's the best approximation to this situation.

Answer:

A. y = 9,958(0.972)x

Step-by-step explanation:

Find the coordinates of point Bon AC such that AB is 1/3 of AC.

Answers

Answer:

(3,3)

Step-by-step explanation:

8--7=15

15/3 = 5

8-5=3

ordered pair at x=3 is (3,3)

If a figure is translated 5 units down and 3 units right, how do you represent it algebraically

Answers

Answer

(x+3) -5

Step-by-step explanation:

plug the values into the parent transformation equation to its rightful places

What is the area of triangle ABC?
O 2.5 square units
O 3 square units
O 3.5 square units
O4 square units

Answers

Answer:

3 square units

Step-by-step explanation:

Edge 2021

The area of triangle ABC will be 3 square units. Therefore, option B is the correct answer.

Triangle ABC in the figure below, where b= 3 units and h= 4 units.

The area of the triangle ABC= The area of the right triangle ABD - The area of the right triangle ACD

We know that, area of a triangle = 1/2 ×Base×Height

The area of the right triangle ABD

= 1/2 ×3×4

= 6 square units

The area of the right angled triangle ACD

= 1/2 ×3×2

= 3 square units

Now, difference = 6-3 = 3 square units

Therefore, option B is the correct answer.

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Domain represents which of the following?
A. slope
B. x values
C. y values
D. maximum

Answers

Answer:

b

Step-by-step explanation:

13 lb7 oz
+ 10 lb2 oz

Answers

Answer:

23Ib9 oz

Step-by-step explanation:

13+10=23

7+2+9

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