A petri dish has 10, 000 bacteria in it. After 4 hours the bacteria’s population increased to 20,000. If the number of colonies grows exponentially, write a formula for the number of bacteria in the dish at any time t, where t is in hours

Answers

Answer 1

Answer:

[tex]P(t) = 10000e^{0.1733t}[/tex]

Step-by-step explanation:

The population of bacteria grows exponentially, which means that it can be represented by a function in the following format:

[tex]P(t) = P(0)e^{rt}[/tex]

In which P(0) is the initial population and r is the growth rate.

A petri dish has 10, 000 bacteria in it.

This means that [tex]P(0) = 10000[/tex]. So

[tex]P(t) = 10000e^{rt}[/tex]

After 4 hours the bacteria’s population increased to 20,000.

This means that [tex]P(4) = 20000[/tex], and we use this to find the growth rate. So

[tex]P(t) = 10000e^{rt}[/tex]

[tex]20000 = 10000e^{4r}[/tex]

[tex]e^{4r} = \frac{20000}{10000}[/tex]

[tex]e^{4r} = 2[/tex]

[tex]\ln{e^{4r}} = \ln{2}[/tex]

[tex]4r = \ln{2}[/tex]

[tex]r = \frac{\ln{2}}{4}[/tex]

[tex]r = 0.1733[/tex]

So, the formula is given by:

[tex]P(t) = 10000e^{0.1733t}[/tex]

Related Questions

If (x + 1)(x - 5) = -9, then which of the following statements is true?
A x+1=0 or x-5=0
B x+1=9 or x-5=-9
C x-2=0

Answers

Answer:

B, although i believe that you wrote wrong, it should be x+1= -9, instead of positive 9

Step-by-step explanation:

Prove: The square of a number that is
one more than a multiple of 3 is also one
more than a multiple of 3.
n +
(3n + 1)2 = [ ? ]n? +
1([ ]n2 +
=
)n) +
- 1 more than a multiple of 3

Answers

Let 3n + 1 denote the "number" in question. The claim is that

(3n + 1)² = 3m + 1

for some integer m.

Now,

(3n + 1)² = (3n)² + 2 (3n) + 1²

… = 9n² + 6n + 1

… = 3n (3n + 2) + 1

… = 3m + 1

where we take m = n (3n + 2).

Two sides of a triangle have the same length. The third side measures 6 m less than twice the common length. The perimeter of the triangle is 14 m. What are the lengths of the three sides?
What is the length of the two sides that have the same length?

Answers

Answer: 5

Step-by-step explanation:

x = common side length

2x + (2x - 6) = 14

4x - 6 = 14

4x = 20

x = 5

I'm supposed to solve for PQ. it's pythagorean theorem.

Answers

Answer:

29 i think

Step-by-step explanation:

pythagoreon thereom is a^2+b^2=c^2 so c^2 being the hypotneuse you would do 2*2=4 +5*5=25 and 4+25=29

Find g(x), where g(x) is the translation 6 units up of f(x)=x2. Write your answer in the form a(x–h)2+k, where a, h, and k are integers.

Answers

Answer:

g(x) = x²+6

Step-by-step explanation:

g(x) = f(x)+6 = x²+6

P+45267=87012 evaluate

Answers

Answer:

p+45267=87012

We move all terms to the left:

p+45267-(87012)=0

We add all the numbers together, and all the variables

p-41745=0

We move all terms containing p to the left, all other terms to the right

p=41745

the target temperature for a laboratory is 71° f. it can vary by up to 3°. if t is the temperature in the laboratory, which of the following inequalities represents this situation?

Answers

Answer:

|t-71| < 3

Step-by-step explanation:

The inequalities represents this situation is | t - 71 | < 3 .

What is inequality?

An inequality is a relation which makes a non-equal comparison between two numbers or other mathematical expressions. It is used most often to compare two numbers on the number line by their size

According to the question

The target temperature for a laboratory = 71° f.

it can vary by up to 3°. (highest limit)

the temperature in the laboratory represented by t

Now,

inequalities represents this situation is

| t - 71 | < 3

Hence, the inequalities represents this situation is | t - 71 | < 3

To know more about inequalities here:

https://brainly.com/question/20383699

#SPJ2

5. Emma, Brandy, and Damian will cut a rope that is 29.8 feet long into
3 jump ropes. Each of the 3 jump ropes will be the same length. Write a
division sentence using compatible numbers to estimate the length of
each rope

Answers

Answer:

29.8÷3=9.93333333333

Step-by-step explanation:

Answer:

Both Question (bottom right corner)

Step-by-step explanation:

Question 2 is obviously a variable because the amount of goals you can score in a game varies, one game it could be 10 then next it could be 5, But for question 1 the amount of work hours she puts in, (assuming she choses when to work and when not to) is also a variable because the amount she works varies from day to day.

Both these examples how data that varies from day to day.

Hope this helps!

John has a rectangular field that is 12 meters by 6 meters, if he wants to divide the field into 8 sections, what would the area per section be?

Answers

Answer:

9 Meters Squared

Step-by-step explanation:

First multiply 6 by 12 to find the area of the whole field:

[tex]6*12=72[/tex]

Then divide that area by 8:

72/8=9

So:

9 meters squared

What is the standard deviation of this data set?
12, 14, 9, 11, 10, 15, 16, 12, 7, 14

Answers

Answer:

The standard deviation is 2.6832815729997

Step-by-step explanation:

SD^2=(12-12)^2+...+(14-12)^2/10

SD^2=72/10

SD^2=7.2

SD=squeare root of 7.2

SD=2.6832815729997

I need to find the measure of PTR

Answers

Answer:

∠ DTR = 109°

Step-by-step explanation:

∠ DQT and ∠ TRS are alternate angles and are congruent, then

∠ TRS = 68°

The exterior angle of a triangle is equal to the sum of the 2 opposite interior angles.

∠ DTR is an exterior angle of Δ TRS , then

∠ DTR = 41° + 68° = 109°

If the angle tis 42 and RS is 9 find QS. Round to the nearest tenth.
Q
R

Answers

Answer:

QS is 12.1

Step-by-step explanation:

9 / sin 48 = QS / sin 90

QS = 9 / sin 48 = 12.1

Determine 0.929229222922229222229

Answers

Answer:

0.93

Step-by-step explanation:

You should try to limit your overall debt to 50% of your gross monthly

Answers

Incomplete question.

At Manning's favorite ice cream shop, a customer can have a cake or sugar cone, vanilla, chocolate, or strawberry ice cream, and chocolate or rainbow sprinkles. How many different ice cream cones can be ordered if the customer chooses 1 cone, 1 type of ice cream, and 1 type of sprinkles?

Answers

Answer:

Step-by-step explanation:

2-cones

3-ice cream flavors

2-sprinkles

2 x 3 x 2 = 12

plz mark brainliest :)

FIND THE MEASURE OF ANGLE 2 PLEASE HELP ASAP!

Answers

Answer:

We know that the figure has a symmetry

angle 1 = angle 2

angle 1 =180°-(18°+90°) = 180° - 108°=72°

Therefore, angle 2 =72°.

Write the point-slope form of an equation of the line through the points (-4, 7) and (5, -3).
A. y−5=−109(x+3)
B. y−7=−109(x+4)
C. y+3=−109(x+5)
D. y+4=−109(x−7)

Answers

Answer:

y+4=–109(x-7)

please mark as brainliest

who ever helps gets brainliest.

Answers

Answer:

B is the answer

Step-by-step explanation:

Answer:

0.0125 dollars per sales

hope this helps

Step-by-step explanation:

Answer:

7.89 i believe i looked it up

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