A culture of bacteria contains 1,500 bacteria initially and doubles every 30 minutes.
1. Write a function that models the number of bacteria after t time.
2. Find the number of bacteria after 2 hours.
3. After how many minutes will there be 12,000 bacteria

Answers

Answer 1

if the bacterial is doubling, that means the growth rate is 100%, or 100% plus whatever it was before, so

[tex]\textit{Periodic/Cyclical Exponential Growth} \\\\ A=P(1 + r)^{\frac{t}{c}}\qquad \begin{cases} A=\textit{current amount}\\ P=\textit{initial amount}\dotfill &1500\\ r=rate\to 100\%\to \frac{100}{100}\dotfill &1\\ t=minutes\\ c=period\dotfill &30 \end{cases} \\\\\\ A=1500(1 + 1)^{\frac{t}{30}}\implies A=1500(2)^{\frac{t}{30}} \\\\\\ \stackrel{\textit{after two hours, or 120 minutes, t = 120}~\hfill }{A=1500(2)^{\frac{120}{30}}\implies A=1500(2)^4\implies A=24000}[/tex]

[tex]~\dotfill\\\\ \stackrel{\textit{current amount being 12000}}{12000=1500(2)^{\frac{t}{30}}}\implies \cfrac{12000}{1500}=(2)^{\frac{t}{30}}\implies 8=(2)^{\frac{t}{30}}\implies 8=\sqrt[30]{2^t} \\\\\\ 8^{30}=2^t\implies (2^3)^{30}=2^t\implies 2^{90}=2^t\implies 90=t[/tex]


Related Questions

write in point slope form an equation of the line that passes through the given point and has the given slope: (0,1); m= 2

A. y - 0 = 2 (x - 1)
B. y - 1 = 2 (x - 0)
C. y + 1 = 2 (x + 0)
D. y + 0 = 2 (x + 1)

Answers

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[tex]\diamond\large\blue\textsf{\textbf{\underline{\underline{Question:-}}}}\diamond[/tex]

         Write an equation for the line that passes through (0, 1) and has a slope of 2 (in point-slope form).

[tex]\diamond\large\blue\textsf{\textbf{\underline{\underline{Answer and How to Solve:-}}}}\diamond[/tex]

Point-slope form:-

      [tex]\sf{y-y_1=m(x-x_1)}[/tex]

Substitute 1 for y₁, 2 for m, and 0 for x₁:-

[tex]\sf{y-1=2(x-0)}[/tex]

So we conclude that Option B is correct.

Good luck.

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Dave wants to buy a classic leather flight jacket that is being sold for $60 less than the normal price. if the jacket normally costs $300, by what percent is it being discounted?
(the answer to your equation will be a decimal. don't forget to convert your answer to a percent)

Answers

Answer: 500%

Step-by-step explanation: 300/60 = 5

5 = 500%

To check work:

60*5 = 300

How can you prove that csc^2 θtan^2 θ-1=tan^2 θ?

Answers

[tex]\stackrel{\textit{Pythagorean Identities}}{1+tan^2(\theta)=sec^2(\theta)}\implies tan^2(\theta ) = sec^2(\theta )-1 \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ csc^2(\theta )tan^2(\theta )-1~~ = ~~tan^2(\theta ) \\\\[-0.35em] ~\dotfill[/tex]

[tex]csc^2(\theta )tan^2(\theta )-1\implies \cfrac{1}{sin^2(\theta )}\cdot \cfrac{sin^2(\theta )}{cos^2(\theta )}-1\implies \cfrac{1}{cos^2(\theta )}-1 \\\\\\ \cfrac{1^2}{cos^2(\theta )}-1\implies \left[ \cfrac{1}{cos(\theta )}\right]^2-1\implies sec^2(\theta )-1\implies tan^2(\theta )[/tex]

6a+6b Factorise these expressions.

Answers

factor by recognising there is a common factor of 6
so 6a + 6b = 6(a + b )

Solve the following equation for b.

13b = 6b + 14

Answers

Answer: 2

Step-by-Step Explanation:

=> 13b = 6b + 14
= 13b - 6b = 14
= 7b = 14
= b = 14/7
=> b = 2

Therefore, b = 2

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[tex]\diamond\large\textsf{\textbf{\underline{Given question:-}}}[/tex]

                Solve the following equation for b.

13b=6b+14

[tex]\diamond\large\blue\textsf{\textbf{\underline{\underline{Answer and how to solve:-}}}}[/tex]

❖ First of all, we need to make sure that all the variables are on one side (the left-hand side, LHS) and numbers are on the right-hand side, RHS.

Here we have variables on the right-hand side, so we can move that term to the left-hand side, making sure to use the opposite operation:-

13b=6b+14              Subtract 6b on both sides, which results in:-

7b=14                      Divide by 7 on both sides, which results in:-

b=2                         We've found the value of b. Now, we need to check our solution by replacing b with the value of b, 2, and seeing whether or not we end up with a true statement:-

13(2)=6(2)+14                 Multiply.

26=12+14                       Now add.

26=26                          Since the left-hand side does equal the right-hand side, we conclude that our solution, b=2, is correct.

Good luck with your studies.

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What is the constant of proportionality shown in the table?

Answers

The constant of proportionality shown in the table that shows the cost and the number of books is 3.

What is the constant of proportionality ?

When there is a direct proportional relationship, it means that as the value of one variable increases, the value of the other variable also increases. As the number of books increases, the cost increases.

Direct proportion: y = kx

Where:

y = dependent variable k = constant of proportionality x = independent variable

k = y/x

6/2 = 3

To learn more about constant of proportionality, please check: https://brainly.com/question/27573249

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Answer:3

Step-by-step explanation:


2. Triangle EFG is a sketch of a triangular community garden that has an area of 47.1 square feet.

Trigonometric area formula: Area = 1/2 a b sin(C)

To the nearest foot, what amount of fencing is needed to surround the
perimeter of the flower bed?

G E F E= 45 degrees EF=12ft F=62 degrees

Answers

Answer:

32ft

Step-by-step explanation:

Let me know if you have any questions ! (or my sketch is different)

everything was rounded to the nearest foot and due to this the new area is 49.5...

Y=5+x how do we solve for x?

Answers

What is Y because then you can do for example if Y is 15 then we would do 10+5 but if you don’t know what Y is then I will try to work it out tomorrow evening because now it is like 11:33 at night.

a right cylinder has a height of 22 1/4ft and a diameter 2 2/5 times it’s height. what is the volume of the cylinder

Answers

Answer:

                         

Step-by-step explanation:

Answer:

Check Below

Step-by-step explanation:

given things  : 1. height of cone  = 22* 1/4 feet or  89/4 feet

                       2.  diameter of cylinder = 2* 2/5 times of height

                                                          =  12/5 times of height or 12/5 * 89/4

                                                           = 89*3/5 feet

now formula of volume of cone =  Pi R² * H

                                                       = (3.14) ( D/2)² * H

                                                       = (3.14)*  (89*3/10)² * 89/4

                                                       = (3.14) * (26.7)² * 22.25

                                                       = (3.14) * 712.89 * 22.25

                                                       =  (49806.06)

Hope u find this answer Helpful !

4 kg of bananas and 3 kg of apples cost £7.50. 3kg of bananas and 5 kg of apples cost £8.10. work out how much 2kg of bananas and 2kg of apples cost​

Answers

Answer:

£4.20

Step-by-step explanation:

Let :

cost of 1 kg banana = xcost of 1 kg apple = y

Equations formed :

4x + 3y = 7.50 [Equation 1]3x + 5y = 8.10 [Equation 2]

Multiply Equation 1 by 5 and Equation 2 by 3 :

20x + 15y = 37.509x + 15y = 24.30

Subtract the newly formed equations :

11x = 13.20x = 1.20

Finding y :

4(1.20) + 3y = 7.504.80 + 3y = 7.503y = 2.70y = 0.90

Then :

Cost of 1 kg banana = £1.20Cost of 1 kg apple = £0.90

Cost of 2 kg bananas and 2 kg of apples :

2(1.20) + 2(0.90)2(2.10)£4.20

simplify √(x^2-10x+25) if -5≤x<5

Answers

[tex]\\ \rm\Rrightarrow \sqrt{x²-10x+25}[/tex]

[tex]\\ \rm\Rrightarrow \sqrt{x²-5x-5x+25}[/tex]

[tex]\\ \rm\Rrightarrow \sqrt{x(x-5)-5(x-5)}[/tex]

[tex]\\ \rm\Rrightarrow \sqrt{(x-5)(x-5)}[/tex]

[tex]\\ \rm\Rrightarrow \sqrt{(x-5)^2}[/tex]

[tex]\\ \rm\Rrightarrow\pm (x-5)[/tex]

Solution set(for x-5)

{-10,-9,-8,-7,-4,-3,-2,-1,0}

for 5-x

{0,-1,-2,-3,-4,-5,-6,-7,-8,-9,-10}

Answer:

First, simplify the expression under the square root sign by factoring:

[tex]\implies x^2-10x+25[/tex]

[tex]\implies x^2-5x-5x+25[/tex]

[tex]\implies x(x-5)-5(x-5)[/tex]

[tex]\implies (x-5)(x-5)[/tex]

[tex]\implies (x-5)^2[/tex]

Therefore:

[tex]\implies \sqrt{x^2-10x+25}=\sqrt{(x-5)^2}[/tex]

[tex]\implies \sqrt{x^2-10x+25}=\pm(x-5)[/tex]

[tex]\implies \sqrt{x^2-10x+25}=|x-5|[/tex]

As the domain is -5 ≤ x < 5, then:

[tex]\implies y=-x+5[/tex]

and the range is 0 < y ≤ 10

would someone help me 2/3 2/1 8/9 7/9 breast to least​

Answers

Answer:

First of all, it's the Greatest to least! Second of all, 2/1, 8/9, 7/9, and 2/3.

Step-by-step explanation:

2/1 is 2, 8/9 is 1 more ninth than 7/9, and 2/3 is less third than 1.

Answer:

It is 2/1 then 2/3 then 7/8 then 8/9  i hope this helps you friend

Step-by-step explanation:

Which graph below shows the solutions for the linear inequality y2-x+1?

Answers

Answer:

The answer will be 1 + y2 - x

is 3/8 Equivalent to 4/3?
is 4/8 Equivalent to 4/3?
is 6/8 Equivalent to 4/3?
is 7/8 Equivalent to 4/3?

Answers

Answer:

  all are NO

Step-by-step explanation:

No integer ratio with 8 in the denominator can be equal to any integer ratio with 3 in the denominator.

__

The denominators 8 and 3 are relatively prime, so equivalent fractions using them cannot be formed with integers.

The equivalent to 4/3 has a mixed-number numerator that is greater than 8.

  [tex]\dfrac{4}{3}=\dfrac{10\frac{2}{3}}{8}[/tex]

This matches none of the offered choices.

What is the 12th term of the sequence -2,-4,-6,...........-100?

Answers

Answer:

-24

Step-by-step explanation:

The common difference (D) is -2. And A1 is -2. so if you just add -2 to the geometric sequence until A12, you would get -24.

Can someone please help me?

Answers

Answer:

m1= 63°m2=117°m3=63°

Step-by-step explanation:

a straight line equals 180°. so if one side is 117°, the other side would have to add up to 180.

180-117=63

And you can kind on figure out what is the same as the other angles. Hope his helps

Jeremiah paid $5.76 for some pencils at the school store. if each pencil cost $0.18, how many pencils did jeremiah buy?

Answers

Answer:

They bought 32 pencils

Step-by-step explanation:

5.76 divided by 0.18 = 32

se a model to solve: (3 points)

two sevenths plus three sevenths plus one seventh equals

Answers

Answer:

6/7

Step-by-step explanation:

all fractions have a common denominator which allows us to add all numerators and maintain the same denominator. 2+3+1=6, and put it back over 7. so 6/7.

URGENT!! VERY HARD QUESTION. WHAT IS 2+2?? NEED ANSWER RIGHT NOW!!

Answers

Answer:

4

Step-by-step explanation:

2+2=4

2 x (6÷2 +8) -4 Help me ​

Answers

Answer:

22x-4

Step-by-step explanation:

2x(3+8)−4

Simplify  3+8 to 11.

2x×11−4

Simplify  2x times 11 to 22x.

22x−4

Root of 3 time the root of
5

Answers

Answer:

root of 15 or in decimal form 3.87 (rounded)

Step-by-step explanation:

You just multiply both together

-2x + 4y = 12

5x - 2y = 10



To answer please type altogether with no spaces. For example if your answer is negative three positive four, type (-3,4)

Answers

Answer:

(4,5)

Step-by-step explanation:

-2x + 4y = 12

5x - 2y = 10

make them both set to y

4y = 2x + 12 -> y = 1/2x + 3

2y = 5x - 10 -> y = 5/2x - 5

since they're both equal to y, they are equal to each other

1/2x + 3 = 5/2x - 5

2x = 8

x = 4

plug it back in to get y

y = 1/2 (4) + 3

y = 5

Help please i only have 5 mins left on my test please answer this


P(Head, Diamond AND Head, Heart) = ?

Answers

Using it's concept, it is found that the desired probability is given by:

P(Head, Diamond AND Head, Heart) = 1/64.

What is a probability?

A probability is given by the number of desired outcomes divided by the number of total outcomes.

In this problem, each outcome is equally as likely, having a 1/8 probability, and they are independent.

Then:

P(Head, Diamond AND Head, Heart) = 1/8 x 1/8 = 1/64.

More can be learned about probabilities at https://brainly.com/question/14398287

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Which of the following ordered pairs are y-intercepts? Check all that apply.
(4, 0)
(–1, 1)
(0, 0)
(0, –7)
(–2, –2)
(0, –0.25)

.

Answers

(0,0) , (0,-7), (0,-0.25)

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[tex]\diamond\large\textsf{\textbf{\underline{\underline{Question:-}}}}\diamond[/tex]

       Which of the following ordered pairs are y-intercepts?

[tex]\diamond\large\blue\textsf{\textbf{\underline{\underline{Answer and How to solve:-}}}}\diamond[/tex]

All y-intercepts have an x-coordinate of 0.

So a y-intercept looks like this:-

[tex]\sf{(0,b)}[/tex]

Where:-

        b - y-intercept

So we conclude that the right options are:-

[tex]\square\!\!\!\!\!\Large\checkmark[/tex] (0,0)

[tex]\square\!\!\!\!\!\Large\checkmark[/tex] (0, -7)

[tex]\square\!\!\!\!\!\Large\checkmark[/tex] (0, -0.25)

Good luck.

         

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A scientist is interested in the relationship between the number of eggs hatched per day for frogs (y) and temperature. Based on
the collected data, the least-squares regression line is ý = 15.66 +3.58x, where x is the number of degrees by which temperature
exceeds 60 degrees Fahrenheit. Which of the following statements best describes the meaning of the slope of the least-squares
regression line? (3 points)
For each increase of one degree Fahrenheit per day, there is an estimated increase of 15.66 hatched eggs.
O For each increase of one hatched egg, the estimated temperature per day increases by 15.66 degrees Fahrenheit.
O For each increase of one degree Fahrenheit per day, there is an estimated increase of 3.58 hatched eggs.
For each increase of one hatched egg, the estimated temperature per day increases by 3.58 degrees Fahrenheit.
The slope has no meaning because the units of measure for x and y are not the same.

Answers

There is an estimated rise of 3.58 hatched eggs for every one degree Fahrenheit increment every day. Then the correct option is B.

What is the linear system?

A linear system is one in which the parameter in the equation has a degree of one. It might have one, two, or even more variables.

A scientist is interested in the relationship between the number of eggs hatched per day for frogs (y) and temperature.

Based on the collected data, the least-squares regression line is y = 15.66 +3.58x, where x is the number of degrees by which temperature exceeds 60 degrees Fahrenheit.

For each increase of one degree Fahrenheit per day, there is an estimated increase of 3.58 hatched eggs.

Thus, the correct option is B.

More about the linear system link is given below.

https://brainly.com/question/20379472

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Answer: For each increase of one degree Fahrenheit per day, there is an estimated increase of 3.58 hatched eggs

Step-by-step explanation:

took the test :)

What will be the new function g(c) if f(x) = 2^x is translated 2 units down and
3 units left?

Answers

Answer:

The new function is

[tex]g(x) = {2}^{x + 3} - 2[/tex]

Help me please help me

Answers

Answer:

3/10

Step-by-step explanation:

Decimals and fractions are similar 4/5 is 0.8 and 1/2 is 0.5 The F has to be 0.3 to make a 4/5. 0.3 in fraction is 3/10

3^2+ square root of 36-2x10

Answers

Answer:

-5

Step-by-step explanation:

9+6-2*10

15-20

= -5

Please help me, I need an answer as soon as possible.

Answers

Answer:

[tex]\huge\boxed{\sf x = \pm \sqrt{7} }[/tex]

Step-by-step explanation:

Given function:

[tex]f(x)=x^2-7[/tex]

We can also write it as:

[tex]y =x^2-7[/tex]

x-intercept is the point where y = 0

Put y = 0 in the above equation

[tex]0=x^2-7\\\\Add \ 7 \ to \ both\ sides\\\\7 = x^2\\\\Take \ sqrt \ on \ both \ sides\\\\\pm \sqrt{7} =x\\\\x = \pm \sqrt{7} \\\\\rule[225]{225}{2}[/tex]

Which is the equation of a circle with a radius of 3 and a center at (0, 0) A . x ^ 2 + y ^ 2 = 3 B x ^ 2 + y ^ 2 = 6; x ^ 2 + y ^ 2 = 9 D. (x - 3) ^ 2 + (y - 3) ^ 2 = 0; (x + 3) ^ 2 + (y + 3) ^ 2 = 0

Answers

Answer:

x² + y² = 9

Explanation:

circle formula: (x -h)² + (y - k)² = r²

where (h, k) is the center, r is radius

Here given for center: (0, 0)

Identify

h = 0k = 0r = 3

Equation of circle:

(x - 0)² + (y - 0)² = 3²x² + y² = 9
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