AA culture started with 4000 bacteria. after 5 hours it grew to 4800 bacteria. Predict how many bacteria will be present after 15 hours. Round your answer to the nearest whole number. p=ae^kt

Answers

Answer 1

Answer:

p = 6912 after 15 hoursp = 4000·e^(0.036463t)

Step-by-step explanation:

We want to model the growth of a population of bacteria using an exponential function. We find it convenient to use an "exact" exponential function that relies directly on the numbers given in the problem statement. That function has the form ...

  p(t) = (initial population) × (growth factor)^(t/(growth period))

where the "growth factor" is the multiplying factor of the population in period "growth period."

__

Exponential Function (1)

Here, the "growth factor" is 4800/4000 = 1.2, and the corresponding "growth period" is 5 hours. Then the population function can be ...

  p(t) = 4000×1.2^(t/5)

__

Population

The population after 15 hours is ...

  p(15) = 4000×1.2^(15/3) = 4000×1.728

  p(15) = 6912

__

Exponential Function (2)

To change this to the form ae^(kt), we find the value of k to be ...

  k = ln(1.2^(1/5)) = ln(1.2)/5 ≈ 0.036463

Then the desired form of the function for p is ...

  p(t) = 4000·e^(0.036463t)

_____

Additional comment

In the form p=ae^(kt) the value of k is often rounded to 3 or 4 decimal places. We believe that best accuracy is obtained if k has at least the number of significant digits expected in the answer. Here, the population of almost 7000 has 4 significant digits, so we choose to express k to 5 significant figures. That still gives a small error relative to the first formula that is only "corrected" by rounding the result to an integer.


Related Questions

show that the function F(x)=x3 +2x is odd. show all work and explain

Answers

a function is odd if f(-x) = - f(x)

f(x) = x³ + 2x

and

f(-x) = (-x)³ + 2 * (-x) = - x³ - 2x = - (x³+2x) = - f(x)

Answer:

Step-by-step explanation:

tlk here

Luka and Gabby rent a tandem bike for $25/hr.Which value is the dependent variable? Which is the independent variable? Write an equation to represent the relationship between the number of hours, h, and the total cost of c.

Answers

c = 25(h)

dependent variable : They must give $25 per hour.

independent variable: time is independent as no specific time given.

total cost = $25 * hours taken

c = 25 * h

c = 25(h)

Answer:

See below ↓

Step-by-step explanation:

Given

rate of renting a tandem bike = $25/hh = number of hoursc = total cost

Solving

Clearly, as the number of hours does not depend on another variable, h is the independent variableTherefore, c is the dependent variableThe equation is :⇒ c = 25h

The radius of the half dollar in centimeters is shown.
Which of the following is closest to the area of the face of the
half dollar?
A. 12 cm2
B. 15 cm2
C. 28 cm2
D. 735 cm2

Answers

Step-by-step explanation:

12 is your answer

22/7 × 1.95× 1.95

you will get 11.9

round off to get

12

bai

What is the volume of this right prism?

1200 in³

1800 in³

2040 in³

3600 in³
Right triangular prism. The height of the prism is labeled as 15 in. The base of the prism is a triangle with the base labeled as 30 in., the height labeled as 8 in., and the other 2 sides of the triangle labeled as 17 in.



brainleiest whoever answers

Answers

Answer:

1800 in^3

Step-by-step explanation:

A sailboat leaves St. Thomas bound for an island in the British West Indies, 200 miles away. Maintaining a constant speed of 18 miles per hour, but encountering heavy crosswinds and strong currents, the crew finds after 4 hours that the sailboat is off course by 15°.
(a) How far is the sailboat from the island at this time?
(b) Through what angle should the sailboat turn to correct its course?
(c) How much time has been added to the trip because of this? (Assume that the speed remains at 18 miles per hour.)

Answers

The distance of the sailboat from the island at this time will be 131.78 miles.

How to calculate the distance?

The distance of the sailboat from the island will be calculated by using the law of cosines. This will be:

a² = (18 × 4) + 200² - (2 × 72 × 200 cos 15°)

a² = 72 + 200² - (144 × 200 cos 15°)

a = 131.78 miles.

The angle that should be used by the sailboat to correct its course will be:

= 180° - (sin 15°/131.78)

= 180° - 22.95°

= 157.05°

Learn more about distance on:

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Gotten two different answers…is it 18 or 55

Answers

Answer:

18.2%

Step-by-step explanation:

For this, you want to take the amount of 70 year old men that will die in the next 10 years and divide it by the total amount of men.

The table states "number out of 1,000 men" so this means there are 1000 total men in this study.

So:

182/1000 = 0.182 = 18.2%

Vani has a collection of vintage action figures that is worth $140. If the collection
appreciates at a rate of 15% per year, which equation represents the value of the
collection after 2 years?
OV = 140(0.85)
Submit Answer
O V = 140(0.15)
V = 140(1 - 0.15)2
V = 140(1 + 0.15)?

Answers

The equation represents the value of the collection after 2 years is V = 140(1 + 0.15)^2.

What equation represents the value of the collection?

When the value of an asset appreciates,it means that the price of the item increases with the passage of time.

The formula for calculating future value with appreciation is:

FV = P (1 + r)^n

FV = Future value P = Present value R = interest rate N = number of years

V = 140(1 + 0.15)^2.

To learn more about future value, please check: https://brainly.com/question/18760477

Answer:

Step-by-step explanation:

V=140(1+0.15)

2

suppose that a movie rental company supervid charges a $30 subscription fee and $1.5 per movie. lets say that another company megawatch charges $100 subscription fee but only $0.90 per show. what are the cost functions for each company's subscription plan.​

Answers

Answer:

the first on is y=30+1.5x and megawatch is y=100+0.90x

Step-by-step explanation:  

Find the slope of the line that passes through \left(10,8\right)(10,8) and \left(1,9\right)(1,9).

Slope ==

Answers

Answer:

m = -1/9

Step-by-step explanation:

PLEASE HELP ASAP!!!!!

a lower auto insurance deductible usually means a higher __

a.) maintenance cost
b.) max out of pocket
c.) premium
d.) ticket.​

Answers

The deductible is the amount one pays towards the auto insurance

The complete statement is: a lower auto insurance deductible usually means a higher premium

What is deductible?

When an insured loss or disaster happens, the amount one pay towards the loss is referred to as the deductible

As a general rule, the more the deductible, the lower the premium; and vice versa.

This means that: a lower auto insurance deductible usually means a higher premium

Hence, the text that completes the statement is premium

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A point located at (-3, 2) is translated down 4 units. What are the coordinates of the image?

(-3, -2)
(1, 2)
(-3, 6)
(-7, 2)

Answers

Answer:

(-3, -2)

Step-by-step explanation:

When a point is translated, the key words are very important to look at.

Up/down means you are translating the y axis.

Left/right means you are translating the x axis.

So using this key, we can solve.

-------------------------------------------------------------------------------------------------------------

A point located at (-3, 2) is translated down 4 units.

Since the point is going down, we will be translating the y axis. 2-4 is -2.

Since the x is staying the same, the x will be -3.

So your translated points are (-3, -2)

-------------------------------------------------------------------------------------------------------------

I hope this helps!

-No one

If an article is sold for rs 99000 after discount of 10% on marked price and adding 10% of Value added tax VAT find marked price​

Answers

Answer:

100000 rupees

Step-by-step explanation:

x × 0.90 × 1.10 = 99000x = 100000

HELP ITS FOR RIGHT NOW!!!!!
You are building a tabletop. You will use the plan shown, except that you will make all dimensions 2 1/2 time as large. What will be the area of your tabletop?

Answers

Answer:

109.375

Step-by-step explanation:

We need to multiply all of the lengths and widths by 2 1/2 in order to make the dimensions 2 1/2 times larger.

For length:

[tex]5\frac{1}{4}[/tex]  x  [tex]2\frac{1}{2}[/tex] = 13.125 or [tex]13\frac{1}{8}[/tex]

For width:

[tex]3\frac{1}{3}[/tex]  x  [tex]2\frac{1}{2}[/tex] = 8.333 or [tex]8\frac{1}{3}[/tex]

Then to find the area use the equation:

A = l x w (Area = length x width)

And plug in the values:

A = [tex]13\frac{1}{8}[/tex]  x  [tex]8\frac{1}{3}[/tex] = [tex]\frac{875}{8}[/tex] or [tex]109\frac{3}{8}[/tex] or 109.375

Janice wins the lottery and takes a lump sum payment. She receives $14,298,120. She places
$10,000,000 into a money market account receiving 10% annual interest compounded monthly,
how much will be in the account after 1 year?

Answers

Answer:

The total compound interest is $1,047,130.76.

Step-by-step explanation:

The amount of the money received after 1 year is $31384283.7672.

What is the compound interest?

Compound interest is the interest on savings calculated on both the initial principal and the accumulated interest from previous periods.

The formula used to find the compound interest = [tex]A=P(1+\frac{r}{100})^{nt}[/tex].

Given that, principal = $10,000,000, rate of interest =10% and time period = 1 year

Here, A=10,000,000(1+10/100)¹²

= 10,000,000(1.1)¹²

= $31384283.7672

Therefore, the amount of the money received after 1 year is $31384283.7672.

To learn more about the compound interest visit:

https://brainly.com/question/14295570.

#SPJ2

Choose the correct graph of the function y=√x+1.

Answers

Answer:

[A}

Step-by-step explanation:

Graph using the end point and a few selected points.

x     y

0     1

1     2

2  2.41

Graph also below:

Find y intercept

[tex]\\ \rm\rightarrowtail y=\sqrt{x}+1[/tex]

[tex]\\ \rm\rightarrowtail y=0+1=1[/tex]

y intercept=(0,1)

Option A

Sandra makes and sells bracelets. It costs her $2 to make each bracelet, plus a one-time cost of $15 for supplies. She plans to sell each bracelet for $5. Let x represent the number of bracelets. Which equation can be used to find the number of bracelets she needs to sell to break even?
2 x minus 5 x = 15
2 x + 5 x = 15
2 x + 15 = 5 x
5 x + 15 = 2 x

Answers

The equation that can be used to find the number for bracelets she needs to sell to break even would be 2x + 15 = 5x

What is the MAD of this data ? Round to the nearest hundredth. 7, 14, 15, 9, 11, 14, 11, 10, 17​

Answers

2.67

Step 1 :

Find the mean of the data :

(2+4+6+8) / 4 = 20/4 = 5

Step 2 :

Find the distance between each data and mean.

Distance between 2 and 5 is 3

Distance between 4 and 5 is 1

Distance between 6 and 5 is 1

Distance between 8 and 5 is 3

Step 3 :

Add all the distances :

3+1+1+3 = 8

Step 4 :

Divide it by the number of data :

8 / 4 = 2

2 is the average absolute deviation.

So hence, your answer is 2.67

"The beautiful thing about learning is that no one can take it away from YOU"

B.B.King

I need step by step written answer for this​

Answers

Answer:

-1/2

Step-by-step explanation:

2/5 * - 3/7 - 1/14 - 3/7 * 3/5

= - 6/35 - 1/14 - 9/35

= - (6*2)/(35*2) - (1*5)/(15*5) - (9*2)/(35*2)

= - 12/70 - 5/70 - 18/70

= (-12 - 5 - 18)/70

=- 35/70

= - 1/2

2/5 * - 3/7 - 1/14 - 3/7 * 3/5
- 6/35 - 1/14 - 9/35
- (6*2)/(35*2) - (1*5)/(15*5) - (9*2)/(35*2)
- 12/70 - 5/70 - 18/70
= (-12 - 5 - 18) /70
=- 35/70
- 1/2

Select the correct answer from each drop-down menu.
Look at the expression below.



Where could parentheses be placed in the expression for it to equal 4?

Where could parentheses be placed in the expression for it to equal 358?

Answers

The expression that the question is referring to is not visible. Sorry, I couldn’t give you a more valid answer.

If 15 percent of cars are blue and an observer's observation is 80 percent accurate, what is the probability that a car is, in fact, blue when the witness reports it as blue

Answers

The probability that a car is blue is the likelihood of the car being blue

The probability that a car is, in fact, blue when the witness reports it as blue is 12%

How to determine the probability?

The given parameters are:

P(Blue) = 15%

P(Accurate) = 80%

The probability that a car is blue, and the observation is accurate is calculated as:

P(Blue and Accurate) = P(Blue) * P(Accurate)

This gives

P(Blue and Accurate) = 15% * 80%

Evaluate the product

P(Blue and Accurate) = 12%

Hence, the probability that a car is, in fact, blue when the witness reports it as blue is 12%

Read more about probability at:

https://brainly.com/question/25870256

A wire 26 cm long is cut into two pieces. The longer pieces is 2 cm longer the the shorter peice.
Find the length of the shorter peice of wire _________ cm

Answers

Answer:

26÷2=13 so if the longer one is 2 cm longer so 13+1 =14. the shorter one is going to be 13-1=12 so 12+14 =26 and the shorter one is 2 cm smaller then the longer one

If the number of equally likely sample outcomes of a single experiment is 4, what is the total number of elements in the sample space if the experiment has 3 stages?

Answers

12 because that’s the answer and yea

PLEASE HELP ME!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

Answers

For x=2

[tex]- 10(2) + y = 4[/tex]

[tex] - 20 + y = 4[/tex]

[tex]y = 24[/tex]

For x=1

[tex] - 10( 1) + y = 4[/tex]

[tex] - 10 + y = 4[/tex]

[tex]y = 14[/tex]

For x=0

[tex] - 10(0) + y = 4[/tex]

[tex]0 + y = 4[/tex]

[tex]y = 4[/tex]

For x=-1

[tex] - 10( - 1) + y = 4[/tex]

[tex]10 + y = 4[/tex]

[tex]y = - 6[/tex]

For x=2

[tex] - 10( - 2) + y = 4[/tex]

[tex]20 + y = 4[/tex]

[tex]y = - 16[/tex]

Answer:

-2 = -16

-1 = -6

0 = 4

1 = 6

2 = 16

Step-by-step explanation:

Find the value of the expression 1/2x+3 if x=12

Answers

Answer:

The answer is 9.

Step-by-step explanation:

1/2 * 12 = 6

6+3=9

Answer:

9

Step-by-step explanation:

x = 12

1/2 · 12 = 6

6 + 3 = 9

A rectangular parking lot has a length that is 9 yards greater than the width. The area of the parking lot is 360 square yards. Find the length and the width.

Answers

Answer: The width is 15 yards and the length is 24 yards

Step-by-step explanation:

Let x represent the width of the parking lot in yards

Let the length of the parking lost be (x + 9) as the length is 9 yards greater than the width

So, area = width * length

i.e. 360 = x(x + 9)

360 = x2 + 9x

x2 + 9x - 360 = 0

x2 + 24x - 15x - 360 = 0

x(x + 24) - 15(x + 24) = 0

(x + 24)(x - 15) = 0

Either x = -24 or, x = 15

But as width can not be negative, so we can not have, x = -24

So, we have, x = 15

Therefore, (x + 9) = (15 + 9) = 24

So, we have the following answers.

Width : 15 yards

Length : 24 yards

1. Shaw High School is having a fundraising event. Products of equal value totaling $480 are sold to an audience of an unknown number of people. The entrance fee is $10.00 per person.
a. What equation gives the total cost per person y as a function of the number of people x, if everyone bought the same amount?
b. How many people must show up in order for the total cost per person to be $16?

HELP MEEEEEEEEEEEEEEEE

Answers

Answer:

10x=480    (x=48)

30 people must show up  for the total cost per person to be $16

Step-by-step explanation:

p= people

10p = 480    

($10 multiplied by the number of people)   10p

p = 48

  48 people bought $10 entrance

     $16 multiplied by the number of people  =16p  

16p = 480

p = 30

 30 people must show up  for the total cost per person to be $16

   

Find the area of the parallelograms below. 21m 33m 21m​

Answers

Answer:

  a. 693²

  b. 148.2 yd²

Step-by-step explanation:

The area of a parallelogram is the product of its base length and the height measured perpendicular to that base.

__

a.

  A = bh = (21 m)(33 m) = 693 m²

__

b.

  A = bh = (19 yd)(7.8 yd) = 148.2 yd²

Help help help help help help math

Answers

Answer:

55

Step-by-step explanation:

Area=LxW

so, Area=11x5

=55

Answeri think its 55

Step-by-step explanation:

you have to multiply 5x11 and thats 55 which is simple becaused i suck at explaining stuff

Find the absolute maximum and minimum, if either exists, for the function on the indicated interval. f (x) = x^4 + 4x^3 - 10 [-2, 2] [-4, 0] [-2, 1] Find the absolute maximum. Select the correct choice below and, if necessary, fill in the answer boxes to complete your choice. The absolute maximum, which occurs twice, is at x = and x =. (Use ascending order.) The absolute maximum is at x =. There is no absolute maximum.

Answers

Answer:

d/dx x^4 + 4x^3 - 10

4x^3 + 12x^2

4x^3 + 12x^2 = 0

x = 0, -3

plug in x if you want the value

Kylie brought 5 pears to soccer practice to share with her teammates. She cuts each pear into thirds. How many slices of pears does she have to share with her teammates? Which equations can you use to solve the problem? Select two equations.
A. 5 × 3 = 15
B. 1/5 × 1/3= 1 /15
C. 1/5 × 3 = 3/5
D. 5 ÷ 1/3 =15
E. 1/3 ÷ 5 = 1/15

Answers

Answer :D

A (or) 5 * 3= 15

Question explanation:

5 pears.

3 pieces

[tex](1 * 3) + (1 * 3) + (1 * 3) + (1 * 3) + (1 * 3)[/tex]

Which is:

[tex](3) * (3) * (3) * (3) * (3)[/tex]

Which, simplified:

[tex]3 * 5[/tex]

Which equals:

[tex]3 * 5 = 15[/tex]

Hope this helps :)  - Answered by Lilo

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