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

Answers

Answer 1

Answer:

c. dP/dt = (1/5)P

Step-by-step explanation:

Given that the rate of change of population with respect to time dP/dt is directly proportional to the population, P, we have

dP/dt ∝ P

dP/dt = kP

Given that dP/dt = 2 million insects per day and P = 10 million insects after 5 days, So,

2 = k × 10

k = 2/10

k = 1/5

So, dP/dt = kP

dP/dt = (1/5)P

Answer 2

The option C is correct

Differentiation

The rate of change of a function with respect to the given variable.

How to get the option?

The rate of change of population with respect to time is directly proportional to the population P. We have

[tex]\dfrac{\mathrm{d} P}{\mathrm{d} t} \propto P\\\\\dfrac{\mathrm{d} P}{\mathrm{d} t} = kP[/tex]

[tex]\dfrac{\mathrm{d} P}{\mathrm{d} t}[/tex] is 2 million insects per day and P = 10 million insects after 5 days. So

[tex]\begin{aligned} \dfrac{\mathrm{d} P}{\mathrm{d} t} &= kP\\2 &= 10k\\k &= \dfrac{1}{5} \\\end{aligned}[/tex]

Then

[tex]\dfrac{\mathrm{d} P}{\mathrm{d} t} = kP\\\\ \dfrac{\mathrm{d} P}{\mathrm{d} t} = \dfrac{1}{5} P[/tex]

Thus, option C is correct.

More about the Differentiation link is given below.

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Related Questions

Evaluate the expression x + 8/27. Evaluate the expression for x=8/9

Answers

Answer: 32/27

Step-by-step explanation:

x = 8/9

x + 8 /27

[tex]\frac{8}{9} + \frac{8}{27} \\\\\frac{8}{9} * 3 = \frac{24}{27}\\\\\frac{24}{27} + \frac{8}{27}\\\\\frac{24 + 8}{27} \\\\\frac{32}{27}[/tex]

Answer:

Substitute the value of the variable into the equation and simplify.

Exact Form:

32 /27

Step-by-step explanation:

ANSWER FAST!

The table shows the linear relationship between the number of right tickets purchased and the total cost of admission plus ride tickets at a carnival. which function can be used to find y, The total cost of attending the carnival in purchasing x ride tickets?

A. Y= 25x +8
B. Y= 8x + 25
C. Y= 8x+ 0.25
D. Y= 0.25x + 8​

Answers

Answer:

c

Step-by-step explanation:

Find the length of x.
a. 33.8
b. 48.3
c. 84.3
d. 72.0

Answers

The length of x is b. 48.3

Find the slope, I don't know how though.​

Answers

Answer:

slope is -2

Step-by-step explanation:

An airline claims that its average taxi time is 15 minutes, and the standard deviation is 1.4 minutes. The taxi time has a bell/mound shape distribution. On a flight with this airline, you observe that the taxi time is 18 minutes. Calculate the z score for your flight's taxi time. Round the final answer to 2 decimal places.

Answers

Answer:

The z score for your flight's taxi time is of 2.14.

Step-by-step explanation:

When the distribution is normal, we use the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

An airline claims that its average taxi time is 15 minutes, and the standard deviation is 1.4 minutes.

This means that [tex]\mu = 15, \sigma = 1.4[/tex]

On a flight with this airline, you observe that the taxi time is 18 minutes. Calculate the z score for your flight's taxi time.

This is Z when [tex]X = 18[/tex]. So

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{18 - 15}{1.4}[/tex]

[tex]Z = 2.14[/tex]

The z score for your flight's taxi time is of 2.14.

You can convert the variate which tracks heights of trees to standard normal variate. That value of standard normal variate is called the z score and shows the area of the considered area in the plot of the standard normal distribution.

The z score for our flight's taxi time is approx 2.14286

How to convert a normal distribution variate to standard normal distribution variate?

Suppose you  have got a normal distribution variate with mean  [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] (let the variate is denoted by X), then we have

[tex]X \sim N(\mu, \sigma)[/tex]

To convert it to standard normal distribution with mean 0 and the standard deviation as 1 ( [tex]Z \sim N(0,1)[/tex] ), we have:

[tex]Z = \dfrac{X - \mu}{\sigma}[/tex]

For the given case we have:

Let the average taxi time be tracked by random variable X, then, as the mean time is 15 minutes, and the standard deviation 1.4 minutes , thus,

[tex]X \sim N(15, 1.4)[/tex]

Converting it to standard variate:

[tex]Z = \dfrac{X - 15}{1.4}[/tex]

Since the observed taxi time was 18 minutes, thus, we have X = 18,

Getting the z score:

[tex]Z = \dfrac{18 - 15}{1.4} = \dfrac{3}{1.4} \approx 2.14286[/tex]

Thus,

The z score for our flight's taxi time is approx 2.14286

Learn more here about normal distribution here:

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how much would 11 trillion divided equally amongst 300 million people be? Time sensitive question

Answers

Answer:

36666.6666667

Step-by-step explanation:

Cant really be equal

Consider that the federal debt is $11 trillion which is divided equally among 300 million people.
To solve the problem mentally, express both in terms of billion.
Since 1 trillion is 1000 billion, so 11 trillion is =11x1000
11,000 billion

Since 1 billion is 1000 million, so 300 million is
300/1000
=0.3 billion

2x-1=7
Not sure how to start to solve this equation

Answers

Answer:

x equals 4. 2x4 is 8-1equals 7

Answer: x=4

Step-by-step explanation: 2x−1=7

2x−1+1=7+1

2x/2=8/2

x=4

Gabrielle's age is three times Mikhail's age. The sum of their ages is 84. What is Mikhail's age?

Answers

Answer: 21

Step-by-step explanation:

84 divided by 4 = 21 since grabielle is 21, and then mikhail is gonna be 3 times more so it’s gonna be 63

Answer:

Mikhail=21

Gabrielle=63

Step-by-step explanation:

G=3M

G+M=84

G=84-M

3M=84-M

4M=84

M=21

G=63

Simplify (0.24) × (-0.15)

Answers

Answer:

0.036

Step-by-step explanation:

Answer:

0.24 x 0.15 = 0.036

Step-by-step explanation:

First ignore the decimal points so you have 24*15 = 360.

You have to start at the right, and move the decimal point 4 places. So, you get 0.036. Pls give brainliest.

Find Principal when Time = 5 years, Interest - $ 500; Rate = 5%

Answers

Answer:

P = $2,000

Step-by-step explanation:

Interest = Principal x Rate x Time

500 = P(.05)(5)

500 = .25P

P = 500/.25

P = 2000


Find the slope and y-intercept of equation y= 10x + 18

Answers

Answer:

slope is 10

y-intercept is 18

Step-by-step explanation:

The slope and y-intercept in y = 10x + 18 are 10 and 18 respectively.

What are lines and their slopes?

We know lines have various types of equations, the general type is

Ax + By + c = 0, and the equation of a line in slope-intercept form is

y = mx + b.

Where slope = m and b = y-intercept.

the slope is the rate of change of the y-axis with respect to the x-axis and the y-intercept is the (0,b) where the line intersects the y-axis at x = 0.

Given a line in slope-intercept form which is y = 10x + 18.

We know in y = mx + b, slope = m, and y-intercept = b.

∴ In  y = 10x + 18.

Slope = 10 and  y-intercept = 18.

learn more about lines and slopes here :

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#SPJ5

Which property is used in the first step to solve this equation
4(x-6)=5
4x-24 = 5
4x= 29
x=29/4

Answers

Answer:

Distributive property

Step-by-step explanation:

4/5×5/6 can you help me

Answers

Answer:

2/3

Step-by-step explanation:

4/5*5/6 =2/3

please mark

Answer:

2/3

(Decimal Form : 0.6)

Step-by-step explanation:

There are 450 student at a school if each classroom codes 30 students How many classrooms are Needed at the school

Answers

Answer:

15 rooms are needed at the school

Step-by-step explanation:

Solve:

Divide 450 (the number of students) by 30 (the number of students per classroom)

450/30= 15

Check your work:

30*15= 450

Hope this helps!

Lavilla is a famous resort in Italy. All of its rooms are always booked in the winter season. On average, 2800 skiers come to the resort every week (7 days). On average, skiers stay in Lavilla for 4 days. Each skier spends $40 daily in local restaurants. Question 1 (1 point) The average number of skiers in Lavilla is: _____________ [skiers].

Answers

Answer:

The average number of skiers in Lavilla are 1,600 skiers

Step-by-step explanation:

The number of skiers that come to Lavilla on average each week = 2,800 skiers

The number of days each skier stays in Lavilla = 4 days

The amount each skier spends in local restaurants daily = $40

According to Little's Law, we have;

L = λ·W

Where;

L = The average number of skiers in Lavilla

λ = The effective arrival rate of the skiers = 2,800 skiers per week arrive

W = The number of days each skier stays at Lavilla = 4 days = 4/7 week

The average number of skiers in Lavilla, 'L', is therefore, given as follows;

L = 2,800 skiers/weel × (4/7) week = 1,600 skiers

The average number of skiers in Lavilla, L = 1,600 skiers

who wants a slushie ?

Answers

Answer:

i want a slushie what's your favorite slushie flavor

What is the leading coefficient of the polynomial f(c) defined below? need help asap!

Answers

Answer: 7

Step-by-step explanation:

The leading coefficient is the number before the term with the highest power in your polynomial. The coefficient is just a number or constant that is before a variable in your expression.

In this case, the highest degree in this polynomial is five. If we look at the coefficient of that term, we see that it is seven.

put a digit in the gap, such that the answer is a whole number 10x + 11 = 144

Answers

Answer:

13.3 or 13

Step-by-step explanation:

10x+11=144

10x=144-11

10x=133

x=133/10

x=13.3

SOMEONE HELP I'LL MARK CORRECT ANSWER BRAINLY

Answers

Answer:

B

Step-by-step explanation:

5r+r= what dose this equal

Answers

Answer:

Step-by-step explanation:

5

How do you determine if a function is even, odd, or neither

Answers

Answer:

You may be asked to "determine algebraically" whether a function is even or odd. To do this, you take the function and plug –x in for x, and then simplify. If you end up with the exact same function that you started with (that is, if f (–x) = f (x), so all of the signs are the same), then the function is even.

Step-by-step explanation:

The next day the gas tank in dad’s car holds 24 gallons. The gas tank in mom’s truck holds 50% less than that. How much gas does the truck’s tank hold?

Answers

24 gallons * 50%

24 gallons * .5

=12

24-12

= 12

thy answer is 12 .

Answer:

Mom's truck would hold 12 gallons.

Step-by-step explanation:

If you take 24 and divide it into 2 parts you would get your answer because 50% would be half of the whole number of that makes any sense

SOLVE: 3x+4y = 18 and -2x+4y = 8

Answers

Answer:

1, if solved for x = 6 - 4y/3 & y = 9/2 - 3x/4

2, x = -4 + 2y & y = 2 + x/2

Step-by-step explanation:

convert the following equation into standard form Y equals negative 7X over 8 +4

Answers

9514 1404 393

Answer:

  7x +8y = 32

Step-by-step explanation:

Clear fractions and add the opposite of the x-term.

  y = -7x/8 +4

  8y = -7x +32 . . . . . multiply by 8

  7x +8y = 32 . . . . . .add 7x

WORTH 20 POINTS!! HELP PLEASEE
The function g(t) = - 16t2 + vt + h represents the height of an object, g, in feet, above the ground in relation to the time, t, in seconds, since the object was thrown into the air with an initial velocity of v feet per second at an initial height of h feet.

A model rocket is launched off the ground at an initial velocity of 80 feet per second.

Part B: What domain makes sense for the function in this context?


1. all positive numbers

2. 0 ≤ t ≤ 100

3. 0 ≤ t ≤ 5

4. all real numbers

Answers

Answer:

Step-by-step explanation:

g(t) = -16t² + vt + h

"rocket is launched off the ground at an initial velocity of 80 feet per second"

v = 80

h = 0

g(t) = -16t² + 80t

:::::

The roots of -16t² + 80t are t=0 and t=5. In other words, the rocket hits the ground after 5 seconds.

Domain: 0 ≤ t ≥ 5

Expand this expression
.-(-5+ +12)

Answers

Answer:

-(-5+12)

opening bracket

-1×-5=5

-1×+12=-12

5+12=17

Answer: = -7

Step-by-step explanation:

you have to remove the + sign and the period and your answer will be -7

Marks car get 32 mpg. He is planning a road trip from Miami to Atlanta. he plans to drive 200 miles. the first day and 480 the next. How many more gallons will he use the second day compared to the first.

Answers

Answer:8.75 gallons

Step-by-step explanation:

well first his car drives 32 mpg, so with this info you divide 200 by 32.Which is 6.25 gallons.Then do the same with 480,480 divided by 32 which is 15 gallons.subtract it 15-6.25 which is 8.75.8.75 more gallons is the answer.

Correct answer:

8.75 more gallons used the second day compared to the first day

What is the value of x in the equation -2 = 5x + 3

Answers

Answer:

-1

Step-by-step explanation:

someone help whats the work for what is 107% of 150

Answers

Answer:

If it's 107% of 50 the answer would be 53.5

If it's 107% more than 50 it would be 103.5

Step-by-step explanation:

107% of 50 is 53.5

50 × 107% = 53.5

50 × 107% = 53.5

+50

--------

103.5

Answer:

160.5

Step-by-step explanation:

you but 107% 150 = what it well give you the answer

Solve for a 4/a+4= -1/a+9

Answers

Answer:

a = -8

Step-by-step explanation:

4/a + 4 = -1/a + 9

-1(a + 4) = 4(a + 9)

-1a - 4 = 4a + 36

-5a - 4 = 36

-5a = 40

a = -8

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