Mathematics High School

In a parenting magazine, Mrs. Smith read an advertisement about all the different ways that bleach can be used to kill bacteria. The advertisement claimed that some forms of bacteria triple in amount after each hour. Consider the situation where one bacterium is found on Mrs. Smith's countertop at home.

Answers

Answer 1

Question:

(a) How many bacteria would be found in 24 hours

(b) How many bacteria would be found in 2 days

Answer:

(a) 282429536481 bacteria

(b) [tex]7.97*10^{22[/tex] bacteria

Step-by-step explanation:

The question illustrates an exponential function

[tex]y = ab^x[/tex]

Where

[tex]a = Initial\ Value = 1[/tex]

[tex]b=Rate = 3[/tex] --- i.e. triples

[tex]x = number\ of\ hours[/tex]

Solving (a): Bacteria in 24 hours

In this case:

[tex]x = 24[/tex]

Substitute [tex]x = 24[/tex], [tex]b = 3[/tex] and [tex]a = 1[/tex]

So:

[tex]y = ab^x[/tex]

[tex]y = 1 * 3^{24[/tex]

[tex]y = 1 * 282429536481[/tex]

[tex]y = 282429536481[/tex] bacteria

Solving (b): Bacteria in 2 days

[tex]2\ days =48\ hours[/tex]

So:

[tex]x = 48[/tex]

Substitute [tex]x = 48[/tex], [tex]b = 3[/tex] and [tex]a = 1[/tex]

So:

[tex]y = ab^x[/tex]

[tex]y = 1 * 3^{48[/tex]

[tex]y =7.97*10^{22[/tex] bacteria

Solving (c): How long for 1000 bacteria

In this case:

[tex]y = 1000[/tex]

Substitute [tex]y = 1000[/tex], [tex]b = 3[/tex] and [tex]a = 1[/tex]

So:

[tex]y = ab^x[/tex]

[tex]1000 = 1 *3^x[/tex]

[tex]1000 = 3^x[/tex]

Take Log of both sides

[tex]Log1000 = Log3^x[/tex]

This gives:

[tex]Log1000 = xLog3[/tex]

Make x the subject

[tex]x = \frac{Log1000}{Log3}[/tex]

[tex]x \approx 6[/tex]

Hence: It takes 6 days

Related Questions

A map represents every 4 miles with 1 inch. If a school and a bank are actually 12 miles apart, how far apart are they on the map, in inches?

Answers

Answer:

Step-by-step explanation:

12÷4=3, so they are 3 inches apart

3 inches
jejsisbuehsuabsibsuababsieb

What is the circumference of a circle whose radius is 1.3 cm? Find the circumference using the formula C=2πr

Answers

Answer:

C≈8.17cm

Step-by-step explanation:

C=2πr=2·π·1.3≈8.16814cm

In the compound interest equation, A(x)= 500(1.07)x, what does the 500 represent?

The starting value

the growth factor

the amount in the account after x years

the annual rate of interest

Answers

Answer:

The starting value.

Step-by-step explanation:

In the compound interest equation A(x)= 500(1.07)x, 500 represents the initial balance, or the starting value.

Jose is going to invest in an account paying an interest rate of 6.1% compounded continuously. How much would Jose need to invest, to the nearest cent, for the value of the account to reach $152,000 in 9 years?

Answers

Answer:

P≈ 87784.11

Step-by-step explanation:

i don't know, I saw the solution on Delta Math

PLEASE HELP ASAP I NEED THIS DONE BY TODAY. ILL GIVE YOU AN ADDITIONAL 50 points. You have to split the shape into two triangles and a rectangle and then add the sums of the areas. HELPPPPPPPPPPPPPPPPPPPPPPPP!!!

Answers

It’s 108 that’s the correct answer

in rst, the measure of t=90°, the measure of r=9°, and tr=2.7 feet. find the length of st to the nearest tenth of a foot.

Answers

Answer:

Step-by-step explanation:

hjjh[tex]\leq[/tex]

Answer:

Step-by-step explanation:

2.7

2.7 9=x

Cross multiply.

x=0.4276

x=0.4276≈0.4 feet

The diagram shows a cuboid.
8 cm
15 cm
20 cm
What is the volume of the cuboid?

Answers

Answer:

mdndmdkdkdkdkd

Step-by-step explanation:

kdkdkdjfjfk

The answer is 2400 cm^3

You just need to multiply the dimensions.

HELPPPPSJSHS
The graph of a quadratic function is shown on the grid below.
Which coordinates best represents the vertex of the graph?

Answers

the best coordinates to represent the graph is (1-1)

Find the value of |5| - 4(3 to the second power - 2).

Answers

Answer:

4.55

Step-by-step explanation:

Answer:

Step-by-step explanation:

1.Find the next three terms in the sequence. -2 , -5 , -8, -11 , ...

2. Find the 100th term.

Please show the working.

Answers

the next 3 terms would be: -14, -17, and -20 (the pattern is your -3 each time) the 100th term would be -279 i think because there is 93 spots left after the first 7 terms, so 93 x -3 = -279

Multiply
7x(x^2-x+2)

Answers

Answer:

7x^3-7x^2+14x

Step-by-step explanation: hope I helped

I need help me please and ASAP!!!!!

Answers

Answer:

C D

Step-by-step explanation:

K/2 simply means k divided by 2. 1/2K also means divided by 2

Answer:C and DHope this helps!! ♥︎

The perimeter of a rectangle is 26 inches. If the length of the rectangle is 6 inches, find the width.

Answers

Answer:

7 inches

Step-by-step explanation:

The perimeter of a rectangle = 2 x ( length + breadth)

26 = 2 x (6 + breadth)

Divide both sides of the equation by 2

26/2 = 6 + width

13 = 6 + width

Collect like terms

13 - 6 = width

width = 7 inches

(3x^4=2x+1)-(2x^4-3x+5)

Answers

Multiply to remove the fraction, then set equal to
0
0
and solve.
Exact Form:
x
=
17
19
x
=
17
19
Decimal Form:
x
=
0.89473684
…
x
=
0.89473684

A fair con is tossed 80 times in an experiment. If the coin is fair, what would be a reasonable number of times tails should appear
based on your knowledge of the theoretical probability of this event?

Answers

Answer: 40 would be a reasonable number of times tails should appear if the coin is fair. Fair means 50/50 chance.

So, divide 80 by 2. 80/2 = 40.

help me fast for extra points

Answers

Answer:

EKH and FKG

Step-by-step explanation:

vertical angles are angles that are directly vertical from each other.

Answer:

Step-by-step explanation:

EKH AND FKG THEY ARE VERTICLE (SAME ANGLES)

what is the 4 one pls help

Answers

Answer:

where are the shapes?

Step-by-step explanation:

Answer:

I think it is 2.5 cm.

Step-by-step explanation:

helppp i really need help will give brainliest

Answers

Answer:

the answers are 13, ab/2, 20 and 15x²/2

Answer:

1/2 a^2, 1/2 b*a , 20, 7.5x^2

Step-by-step explanation:

Area of right angle triangle = 1/2 height * base so

Area of MSP = 1/2 a^2 , Area of BUC =1/2 a*b

Area of BAC =1/2 8*5 , Area of DRK =1/2 3x*5x =1/2 *15x =7.5x^2

HELP ME ON GEOMETRY!!! PLZ
NO LINKS! > i will report.

Answers

Answer

I believe B.)8in3 is the right answer according to the square-cube law.

Step-by-step explanation:

Find the measure of each numbered angle on this Triangle.

Answers

Answer:

m<1 = 69

m<2 = 37

m<3 = 106

m<4 = 21

Step-by-step explanation:

Solve the equation 18+a= -5

Answers

Answer:

The answer is -23

Step

the answer is a = -23

4(−3x+8)=−16 Which value is the solution to the equation below?

Answers

Answer:

I'm 99.9% sure that x=4

Step-by-step explanation:

The answer is X=4 explanation in picture

La suma de las edades de Pedro y su hijo son 84 años. Hace 6 años la edad de Pedro era 3 veces la edad de su hijo.
¿Qué edad tiene el hijo actualmente?
a) 34 años
b) 29 años
c) 24 años
d) 19 años

Es una pregunta de un examen en la que me quede estancado porque me da 32 o otra forma me da 30 pero ninguna es la opcion

Answers

Answer: 24 years old

Find the area in the pic please!!

Answers

Answer:

Area = 970 ft²

Step-by-step explanation:

The shape is composed of a square and a triangle.

Therefore:

Area of the shape = area of square + area of triangle

✔️Area of square = s²

s = 20 ft

Area = 20²

Area of square = 400 ft²

✔️Area of triangle = ½*b*h

b = 20 + 9 + 9 = 38 ft

h = 30 ft

Area of triangle = ½*38*30 = 570 ft²

✅Area of the shape = 400 + 570 = 970 ft²

What is the slope of points (2,-15) and (-3,10).

Answers

Answer:

m = 5

Step-by-step explanation:

I believe you are asking, "What is the slope of the line passing through the points (2, -15) and (-3, 10)?"

As we go from (-3, 10) to (2, -15), x (the horizontal leg of a right triangle) increases by 5 (this is the 'run'), and y (the vertical leg) increases by 25 (the 'rise'). Thus, the slope of this line is

m = rise / run = 25/5, or just 5. m = 5

please help me outt

Answers

Answer:

see explanation

Step-by-step explanation:

The scientific notation is 3.212 · 10^8

5. What is the inverse function of

Answers

Answer:

i think that it is. C.

i think it will help

I also think it’s C
Hope that helps!

a quantity of y varies partly as x and partly as the square of x. when x=2 ,y=14 and when x=5, y=65. Find y when x=-2

Answers

X\times 2 bc it is correct I think I’m not sure but yeah

If the Math Olympiad Club consists of 15 students, how many different teams of 3 students can be formed for competitions?

Answers

Answer:

5 teams

15÷3=5

Have a great day

Answer:

5 teams

Step-by-step explanation:

There are 15 students, and 3 students per team. Divide 15/3 and you get 5.

can someone help with this question please? (no links!!)

Answers

Answer:

Step-by-step explanation:

radius is half of it so 7 times 2= 14 and then multiply by 3.14.

So 43.96

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