The population of a certain species of insect is given by a differentiable function P , where P(t) is the number of insects in the population, in millions, at time t , where t is measured in days. When the environmental conditions are right, the population increases with respect to time at a rate that is directly proportional to the population. Starting August 15, the conditions were favorable and the population began increasing. On August 20, five days later, there were an estimated 10 million insects and the population was increasing at a rate of 2 million insects per day. Which of the following is a differential equation that models this situation?

a. P=2(tâ5)+10
b. dP/dt=2/5t
c. dP/dt=1/5P
d. dP/dt=5P

Answers

Answer 1

Answer:

Option C, dP/dt=1/5P

Step-by-step explanation:

The change is population of insects is directly proportional to the rate of change of population

Hence,

[tex]\frac{dP}{dt} \alpha P[/tex]

Or [tex]\frac{dP}{dt} = kP[/tex]

where K is the proportional constant

We will find the value of k

Keeping the given values of rate of change of population and population in above equation, we get -

[tex]\frac{2}{10} = k\\k = \frac{1}{5}[/tex]

Hence,

[tex]\frac{dP}{dt} = \frac{1}{5} P[/tex]


Related Questions

Find 345 x 6 using expanded form.
300+40+5=345

Answers

Answer:

2,000 + 0 + 70 + 0 = 2,070

Step-by-step explanation:

300 + 40 +5 x 6

300 + 4 = 340

340 + 5 = 345

345 x 6 = 2070

2,000 + 0 + 70 + 0 =

2,070

Hope this helps

What is the value of the expression? 21.18
÷
6 =

ASAP PLEASE

Answers

Answer:

3.53

Step-by-step explanation:

I checked it using a calculator. :)

c)
4 x 4 x 4 x 5 x 5
Write this using index notation

Answers

Step-by-step explanation:

4'3x5'2

It means 4'3= 4 multiplied by its self 3 times

Write a situation for -3x+6>9

Answers

Answer:

-6x+3>9

Step-by-step explanation:

Shift the equation to suitable form

-3x+6>9-(-3x+6)<-93x-6<-9

Suppose you begin with a number . Multiply it with 3 then subtract 6 from it ,describe a suitable no so that the resulting number will be less than -9.

Write the equation of the line that passes through the points (-7,7) and (-6, -5)

Put your answer in fully reduced point-slope form, unless it is a vertical or horizontal
line.

Answers

Answer:

y = -12x -77

Step-by-step explanation:

-5 - -7/-6 - -7 = -12

slope = -12

y = mx + b

Subsutitue

7 = -12 ⋅ -7 + b

b = -77

good luck, i hope this helps :)

Pls help I will give thx and give points

Answers

Answer:

20

Step-by-step explanation:

you use the pathagorian theorem which is a suqared plus b squared equals c squared.

it would be 12*12 plus 16*16 equals x squared. so 144 plus 256. that equals 400. then you take the square root of it which is 20. therefore x equals 20.

In a survey of 314 job recruiters, 46% said that they had reassessed a job candidate after viewing his/her social media profile and content. (This includes both positive and negative reassessments of the job candidate.) Construct a 90% confidence interval for the proportion of job recruiters who reassessed a job candidate after viewing his/her social media content.

Answers

Answer:

The 90% confidence interval for the proportion of job recruiters who reassessed a job candidate after viewing his/her social media content is (0.4137, 0.5063).

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.

[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

In which

z is the zscore that has a pvalue of [tex]1 - \frac{\alpha}{2}[/tex].

In a survey of 314 job recruiters, 46% said that they had reassessed a job candidate after viewing his/her social media profile and content. (This includes both positive and negative reassessments of the job candidate.)

This means that [tex]n = 314, \pi = 0.46[/tex]

90% confidence level

So [tex]\alpha = 0.1[/tex], z is the value of Z that has a pvalue of [tex]1 - \frac{0.1}{2} = 0.95[/tex], so [tex]Z = 1.645[/tex].

The lower limit of this interval is:

[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.46 - 1.645\sqrt{\frac{0.46*0.54}{314}} = 0.4137[/tex]

The upper limit of this interval is:

[tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.46 - 1.645\sqrt{\frac{0.46*0.54}{314}} = 0.5063[/tex]

The 90% confidence interval for the proportion of job recruiters who reassessed a job candidate after viewing his/her social media content is (0.4137, 0.5063).

assume that a student is chosen at random from a class. Determine whether
the events A and B are independent, mutually exclusive, or neither. A: The student is a woman
B: The student belongs to a sorority

Answers

A student is chosen at random from a class ,The student is a woman.

What do you mean random?

lacking a clear goal, plan, or pattern. : created, completed, or picked at random. read a few pages of the book at random. : referring to, containing, or being elements or occurrences that have a known likelihood of occurring.

Known as an entropy source, a TRNG is a function or apparatus that uses randomness to produce non-deterministic data (such as a series of numbers) to seed security algorithms.

As synonyms for random, the words casual and haphazard are frequently used.

straightforward random sampling Choosing a sample with simple random sampling necessitates the use of randomly generated numbers.

Random Sampling with StratificationRandom sampling in a cluster.systematically using random sampling

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Roberto evaluated 34 ÷ 45 and got an answer of 1516. Which statement is true about his answer? Whoever get it right and helps me get brainllest pls

Answers

Answer:

roberto is not smart

Step-by-step explanation:

34/45 is 0.75555555555 or 0.75 or .75

ur welcome

Find the rate of $740 for 5 pounds

Answers

Answer:

Each $148 = 1 pound.

Step-by-step explanation:

How to subtract fractions

Answers

Answer:

Make sure the bottom numbers (the denominators) are the same.

Subtract the top numbers (the numerators). Put the answer over the same denominator.

Simplify the fraction (if needed).

Step-by-step explanation:

"There are 3 simple steps to subtract fractions

Make sure the bottom numbers (the denominators) are the same.

Subtract the top numbers (the numerators). Put the answer over the same denominator.

Simplify the fraction (if needed)."

2+6453433+7/2=? what is the anwcer to this queston. please help

Answers

Answer:

6453438.5

Step-by-step explanation:

calculatorrrrr

Sarah's favorite candy consists of sour patch kids and M&Ms. She has 17 total packages of sour patch kids and M&Ms. She has 5 more packages of sour patch kids than M&Ms. How many packages of each Candy does Sarah have?

Answers

Answer:

Sarah has 11 packages of sour patch kids and 6 packages of M&Ms

Step-by-step explanation:

11 + 6 = 17, and 11 is five more than 6, fulfilling the needs of the problem

Answer:

Sarah has 11 packages of sour patch kids and 6 packages of M&Ms

Step-by-step explanation:

11 + 6 = 17, and 11 is five more than 6, fulfilling the needs of the problem

hope this helps

Audiology is the study and medical treatment of hearing loss. What does the root aud mean?

Answers

aud means “to hear”

~ Hope this helps!


What is the value of x?

x= [?]

Answers

The answer might be 7
I think that’s the answer X=[7]
[1]

Which of the following mortgage options will not have a PMI requirement?
O A. 3/27 balloon mortgage
B. 30-year mortgage
O C. 7/1 ARM
D. 75/25 mortgage

Answers

75/25 mortgage, implies a down payment of 25%, so there would be no PMI requirement.

The correct answer is D.

What is a mortgage?

A mortgage is a type of loan used to purchase real estate or property.

In a mortgage, the borrower (often called the "mortgagor") agrees to pay back the lender (often called the "mortgagee") over a period of time, typically 15 to 30 years.

We have,

A PMI (Private Mortgage Insurance) requirement is typically necessary for mortgages with a down payment of less than 20% of the purchase price of the home.

Now,

75/25 mortgage, implies a down payment of 25%, so there would be no PMI requirement.

3/27 balloon mortgage, and 7/1 ARM, do not relate to the PMI requirement.

A 30-year mortgage would have a PMI requirement if the down payment is less than 20%.

Thus,

75/25 mortgage, implies a down payment of 25%, so there would be no PMI requirement.

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x - 6y -- 2: = -8
--x + 5y + 3 = 2
3x - 2y - 42 = 18

Answers

1. Subtract first equation from second equation:

y = 7, if that first step is simplified.


2. Substitute y = 7 in any of the equations. (I am substituting in the first equation) :

You will get your x, which is x = 36


So now that you have your x and your y, you have finished solving the equation.

The answer is:
(x,y) = (36, 7)


Hope this helped! Have an awesome day!!


Move the numbers to the blanks to order them from least to greatest value.

0.4. 9/8. -2. 1.2. -0.89​

Answers

Answer:

-2.12 -089 0.4 9/8

Step-by-step explanation:

im good at fractions

Ha I think you should do that to you get it done and then I will do that you know if I have a

Mrs. Larson made 12 pillows from 16 yards of the same fabric how much fabric was used to make each pillow between what two whole numbers does your answer lie

Answers

Answer:The answer is given by :

[ The amount of material ]  / [The  number of pillows made ]  =   16 / 12  = 4 /3 = ( 1 + 1/3 ) yds per pillow

So the answer lies between the integers 1 and 2

Step-by-step explanation:

Mr.Fuller wants to put fencing around his rectuangular-shaped yard. The width of the yard is 55 feet and the length is 75 feet. How many feet of fencing does Mr.fuller need

Answers

Answer: 22% fencing

Step-by-step explanation:

Mr. Fuller needs 260 feet of fencing to put around his rectangular yard.

What is the perimeter?

Perimeter is the measure of the figure on its circumference.

Here,
To find the perimeter of the rectangular yard, we need to add up the lengths of all four sides.

The two sides that are 55 feet long are the width of the yard, and the two sides that are 75 feet long are the length of the yard.

So, the perimeter of the yard is:

Perimeter = 2 × (length + width)

Perimeter = 2 × (75 feet + 55 feet)

Perimeter = 2 × 130 feet

Perimeter = 260 feet

Therefore, Mr. Fuller needs 260 feet of fencing to put around his rectangular yard.

Learn more about perimeter here:

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Please help me i don’t have much time left please

Answers

8 cubed means each side is 2 inches. The first box is 2 inches.

Larger shipping box has each side + 6 more inches so 2 + 6 is 12. The volume is 12 times 12 times 12 which is 1728 inches squared.

If the box with a side length of 2 can carry 1 golf ball then a box with the side length of 6 can carry 3 golf balls because 6/2 is 3. The answer for the last box is 3.

2

1728

3

3х+2 / 4 - 2x+1 / 3= 5


Answers

Answer:

X= 25/6

Step-by-step explanation:

Please mark brainliest

CAN ANYONE HELP ME I WILL MARK AS BRAINLIEST
Solve the word problem and Write the statements.
Grade 3 students used three rolls of ribbons measuring 300 metres, 286 metres and 258 metres for dance in primary Concert. Find the total length of ribbons.

Answers

Total length of ribbons = 300+286+258
= 844 meters

What is sales tax and explain how we use it in everyday life.
1-5 sentences plz

Answers

Answer: Look below. I hope this helps=3

Step-by-step explanation: Sales tax is an additional amount of money you pay. based on a percentage of the selling price of goods. Also services that are purchased. For example, if you purchase a new television for $400 and live in an area where the sales tax is 7%. Then you would pay $28 in sales tax.

Can someone explain this to me? Pls

Answers

Step-by-step explanation:

In Triangle (the symbolΔ)QRS,

Angle R is congruent to Angle Q,

And side QR=11

And side SQ=8

Find.The length of RS.

Is the set of ordered pairs above a function? {(3,4), (1,5), (-9,0), (3,-2)}

Answers

Answer:

not a function

Step-by-step explanation:

{(3,4), (1,5), (-9,0), (3,-2)}

This is not a function since the input 3 goes to two different outputs

3 goes to 4 and -2


help me please I have 10 minutes to do this

Answers

Answer:

Distributive

Step-by-step explanation:

The 4y is distributed to the terms in parentheses.

Bill from Bill's Burgers raises the price of his bacon cheeseburger by 15%. If the old price was $6, what is the new price?

Answers

Answer:

$6.90

Step-by-step explanation:

$6 * .15 = $0.90

$6 + $0.90= $6.90

Answer:

$6.90

Step-by-step explanation:

6 x 1.15 = 6.9

= $6.90

Was Perry’s hypothesis correct? Explain

Answers

Answer:

yes he was correct Perry's hypothesis was correct

The fractions and decimals in order from least to greatest 7/48 0.5 0.75 9/16

Answers

Answer:

7/48,0.5,9/16,0.75

Step-by-step explanation:

Hope this helps

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