Bacteria growth. A colony of bacteria is grown under ideal conditions in a laboratory so that the population increases exponentially with time. At the end of 3 h there are 10,000 bacteria. At the end of 5 h there are 40,000 bacteria. How many bacteria were present initially

Answers

Answer 1

Answer:

1250 bacteria

Step-by-step explanation:

The formula for Exponential Growth is given as:

P(t)= Poe^rt

Where

P(t) = Population after time t

Po = Initial Population

r = growth rate

t = time

Hence, solving for the above question , we have to find Po

Making Po the subject of the formula

Po = P(t)/e^rt

Step 1

Find the Exponential growth rate

At the end of 3 h there are 10,000 bacteria.

Hence:

Po = 10000/e^3r.... Equation 1

At the end of 5 h there are 40,000 bacteria.

Po = 40000/e^5r..... Equation 2

Equating both equations together,

10000/e^3r = 40000/e^5r

Hence:

e^5r/e^3r = 40000/10000

e^2r = 4

Take the In of both sides

In (e^2r) =In 4

2r= In 4

r = In 4/2

r = In 2

Step 2

Solve for Po(Initial Population)

Using Equation 2

Po = 40000/e^5r..... Equation 2

r = In2

Po = 40000/e^5 × In 2

Po = 40000/2⁵

Po = 1250 bacteria.

Therefore, they was 1250 bacteria initially


Related Questions

The Maxwell family goes out for dinner. The price for the
meal is $90. The sales tax on the meal is 7.25% and they
also want to leave an 18% tip. What is the total cost of the
meal?

Answers

Answer:

$113.90

Step-by-step explanation:

Find the cost of the meal with sales tax:

90 x 0.075 = 6.525

Add that to the original cost of the meal:

90 +  6.525 = 96.525

Find the cost of the tip:

96.525 x 0.18 = 17.3745

Add the tip to the meal price:

96.525 + 17.3745 = 113.8995

Round to get your final answer

113.90 with exact change

are behind on your classes?

Answers

yes. how'd you knowwww?

Answer:

no

Step-by-step explanation:

PLEASE HELP

What is 2/3 of 15% of $2,000?
F. $100
G. $200
H. $300
J. $450
K. $500

Answers

Answer:

$200 dollars my friend.

Step-by-step explanation:

Hope I helped!

The solution is Option G.

The value of the equation A = ( 2/3 ) x 15% x $ 2000 = $ 200

What is an Equation?

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be represented as A

Now , the value of A is

Substituting the values in the equation , we get

A = ( 2/3 ) x 15% x 2000   be equation (1)

On simplifying the equation , we get

A = ( 2/3 ) x ( 15/100 ) x 2000

A = ( 2/3 ) x ( 15 ) x ( 20 )

On further simplification , we get

A = ( 2/3 ) x 300

A = 2 x 100

A = $ 200

Therefore , the value of A is $ 200

Hence , the equation is A = $ 200

To learn more about equations click :

https://brainly.com/question/19297665

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Which of the following values of n will result in a true statement when
substituted into the given equation?
2n + 4 = 12
A n = -1
B n = 0
C. n = 4
D. n = 6

Answers

Answer:

C. n=4

Step-by-step explanation:

got it

how does energy from the sun travel to earth ?​

Answers

Answer:

the heat.. energy is heat and when its hot outside thats the energy from the sun

Helpppp meeeeeee plsssss

Answers

Answer:

Domain: [-4, ∞)

General Formulas and Concepts:

Algebra I

Domain is the set of x-values that can be inputted into function f(x)

Step-by-step explanation:

According to the graph, our line's x-values span from -4 to infinity. Since -4 is closed dot, it is inclusive in the domain:

Interval Notation: [-4, ∞)

Interval Notation: y ≥ -4

which of the following in an organic molecule
A.salt
B.lipid
C.carbon dioxide
D.water

Answers

Answer:

B. lipid is an organic molecule

PLEASE HELP THIS IS TIMED

consider functions f and g.
[tex]f(x) = 3 \sqrt{x} + 1[/tex]

(SEE IMAGE ABOVE)
what is the value of f(g(1))​

Answers

Answer:

f(0) = +1

Step-by-step explanation:

g(1) for x = 1 is Zero .

Substitute it into the function f(x) then you will get 1.

PLS HELP FOR BRIANLIST!!!! There are 8 more students in a math class than in a history class. If the ratio of the students in the math class to the history class students is 9 : 7, how many students are in math class?

Answers

Answer:

9-7= 2

8 / 2 = 4

4 X 9 = 36

4 X 7 = 28

36 students in math class

Answer:

36 students in the math class

Step-by-step explanation:

Brady needs to cut a piece of scrapbook paper
12 centimeters long. He cuts pieces of the following
lengths. Which cut results in a percent error of 15%?
Select all that apply.

Answers

It is 10.2 centimeters so option A :)

Answer:

Option A and Option C

Step-by-step explanation:

If we know that we have to cut a peice of paper 12 centemiters long, that means a 15% error would be cutting out one of the following lengths....

12 - 12(0.15) = 10.2 cm

or

12 + 12(0.15) = 13.8cm

So from this, we see that the answers are Option A and Option C  

Jane spends about 1/6 of the day sleeping. How many hours in a day does Jane sleep? How many hours in a week?

Answers

Answer:

Jane spend 4 hours in a day sleeping, and 28 hours in a week.

Step-by-step explanation:

In 1 day, there are 24 hours. 24 multiplied by 1/6 is 4. I know this because 24 x 1/6 = 24/1 x 1/6 = 24/6 = 4/1 = 4.

In 1 week, there are 168 hours. 1/6 multiplied by 168 is 28. I know this because 168 x 1/6 = 168/1 x 1/6 = 168/6 = 28/1 = 28

I would appreciate brainliest.

Please help on this will mark the first answer brainliest

Answers

Answer:

The equation is 3n + 13 = 40 The triplets are 9 years old

Step-by-step explanation:

~Help, please-~
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Also out of all these boys which one do you think is the [tex]cutest[/tex]?
1. Katsuki Bakugou
2. Eijiro Kirishima
3. Izuku Midoriya
4. Denki Kaminari
5. Tenya Ida
6. Yuga Aoyama
7. Mashirao Ojiro
8. Koji Koda
9. Rikido Sato
10. Mezo Shoji
11. Hanta Sero
12. Fumikage Tokoyami
13. Shoto Todoroki
14. Minoru Mineta
15. Tamaki Amajiki

Answers

Answer:

never heard of them

and the answer is choice B.

Step-by-step explanation:

alternate exterior angles have the same measure

The answer would be c

in a school, 56% of the 850 students are girls. work out the number of girls in the school

Answers

Answer:

476 girls

Step-by-step explanation:

total students : 850

56% of 850 = 476

Help me mdkskkeeknsjeleksksk

Answers

Answer:it’s an unknown number

Step-by-step explanation:

please answer now i am being timed ​

Answers

You should substitute the values of x and y from the suggested points into the given equation and if both sides are equal then the point is on that line.
Using this, the points are (-5,5), (1,2), and (5,0)

If f(x) = 5 + 4(x - 4)?,
what is f(7)?

Answers

Answer:

Let's solve for f.

x=5+4(x−4)f(7)

Step 1: Flip the equation.

28fx−112f+5=x

Step 2: Add -5 to both sides.

28fx−112f+5+−5=x+−5

28fx−112f=x−5

Step 3: Factor out variable f.

f(28x−112)=x−5

Step 4: Divide both sides by 28x-112.

f(28x−112)28x−112=x−528x−112

f=x−528x−112

Answer:

f=x−528x−112

A bank offers an annual simple interest rate of 6% on home improvement loans. How much would Tobias OWE IN ALL if he BORROWED $12,000 over a period of 3 years?

Answers

Answer: $14160

Step-by-step explanation:

Simple interest would be calculated as:

= PRT/100

where,

P = Principal = $12000

R = Rate = 6%

T = Time = 3 years

Simple interest = ($12000 × 6 × 3)/100

= $216000/100

= $2160

The amount that Tobias owe in all would be:

= $12000 + $2160

= $14160

PLEASE HELP QUICK
Solve 3/10n - 3 1/5= -1 1/5.

n = 8
n = - 6/25
n = 6 2/3
n = -12 2/3

Answers

Answer:

It is 6 and 2/3

Step-by-step explanation:

Hope this helps

Answer:

6 2/3

Step-by-step explanation:

Credits to the person above :)

What will be the answer in the finish box

Answers

Answer:

Step-by-step explanation:

In the first triangle, using Pythagorean's theorem, x^2+3^2=5^2, x = 4

In the second triangle, using Pythagorean's theorem, x^2+7^2=24^2, x = 25

In the third triangle, using Pythagorean's theorem, 8^2+15^2=x^2, x = 17

In the fourth triangle, using Pythagorean's theorem, x^2+8^2=10^2, x = 6

In the fifth triangle, using Pythagorean's theorem, 5^2+12^2=x^2, x = 13

Evaluate the function f(x) = 3x-5 when x= -3
f(-3)

Answers

aaaaaaaaaaaaaaaaaaaaaaa

If two angles of a triangle have measures 42∘ and 20 ∘ what is the measure of the third angle?

Answers

Answer:

[tex]x = 118[/tex]

Step-by-step explanation:

[tex]42 + 20 + x = 180[/tex]

[tex]62 + x = 180[/tex]

[tex]x = 180 - 62[/tex]

[tex]x = 118[/tex]

Which expression shows 18 + 15 written as a product of two factors?
3(6+5)
6(3+5)
3(9+5)
6(3+2)

Pls help

Answers

The expression that shows 18 + 15 as a product of two factors is 3(6 + 5)

How to rewrite the expression as a product?

The expression is given as:

18 + 15

Factor out 3 from the expression

18 + 15 = 3 * (6 + 5)

Hence, the expression that shows 18 + 15 as a product of two factors is 3(6 + 5)

Read more about expressions at:

https://brainly.com/question/723406

#SPJ2

A plane leaves at 11:22 a.m. and arrives at 3:13 p.m. How long was the flight?

A. 3 hours and 51 minutes long
B. 3 hours and 35 minutes long
C. 14 hours and 35 minutes long
D. 4 hours and 35 minutes long
E. 8 hours and 9 minutes long​

Answers

the answer would be A

Answer:

A. 3 hours and 51 mins long

Step-by-step explanation:

22-13= 9 min difference

11-3=4 but since there is a 9 min difference it would be 9 mins away from 4 hours so that why is it 3 hours and 51 minutes long

hope this wasnt confusing

Plz help I am failing in math and only have a week!!

Answers

Answer:

11. Slope of the line is 7/10.

12. Slope of the line is [tex]-\frac{1}{3}[/tex]

Step-by-step explanation:

11. Given points are:

(-6, 1) and (4, 8)

Slope of a line is given by the formula;

m = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]

m = [tex]\frac{8-1}{4-(-6)}[/tex]

m = [tex]\frac{7}{4+6}[/tex]

m = [tex]\frac{7}{10}[/tex]

Slope of the line is 7/10.

12. Given points are:

(2, -3) and (5, -4)

Slope of the equation is;

m = [tex]\frac{-4-(-3)}{5-2}[/tex]

m = [tex]\frac{-4+3}{3}[/tex]

m = [tex]\frac{-1}{3}[/tex]

Hence,

Slope of the line is [tex]-\frac{1}{3}[/tex].

what is the domain of this function? 
x
2
5
8
11
14
17
20
y
1
3
7
13
21
31
43
answer soon please ty!!!

Answers

Answer:

no real numbers

Step-by-step explanation:

4(f + 1) = 12
what does f equal

Answers

Answer:

f=2

Step-by-step explanation:

4(f+1)=12

4f+4=12

-4 -4

4f=8

f=2

Answer

F = 2

Step-by-step explanation:

Distributive property: 4f+4=12

-4 -4

Subtraction property of equality: 4f=8

/4. /4

Division property of equality: f=2



60% of what number is equal to 30?

Answers

Answer:

50

Step-by-step explanation:

60% of 50 is 30

60% of 30 is 18 because the rest of the 40% would equal 18+? Anonymous

Find the perimeter in simplest form and explain your work

Answers

9514 1404 393

Answer:

  7 1/8 yd

Step-by-step explanation:

The perimeter is the sum of the three side lengths. They are all the same, so we can use multiplication to find their sum.

  P = 3·(2 3/8 yd) = 6 9/8 yd  . . . . .  9/8 = 1 1/8

  P = 7 1/8 yd

The perimeter is 7 1/8 yards.

Answer:

[tex]perimeter \: of \: the \: triangle \\ = 2 \frac{3}{8} +2\frac{3}{8} + 2 \frac{3}{8} \\ = 3 \times 2 \frac{3}{8}\\= 3 \times \frac{19}{8} \\ = \frac{57}{8} \: yd \\ = 7 \frac{1}{8} \: yd[/tex]

57/8 yards is the right answer.

please help 20 points ---> Which statement about the Great Compromise is accurate?

A. It included all of Edmund Randolph’s ideas.
B. It was a completely new and different plan.
C. It overlooked the issue of state representation.
D. It merged the ideas of multiple delegates’ plans.

Answers

Answer: B. It was a completely new and different plan.

Step-by-step explanation:

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