1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
USPshnik [31]
3 years ago
13

Verify that P = Ce^t /1 + Ce^t is a one-parameter family of solutions to the differential equation dP dt = P(1 − P).

Mathematics
1 answer:
NemiM [27]3 years ago
3 0

Answer:

See verification below

Step-by-step explanation:

We can differentiate P(t) respect to t with usual rules (quotient, exponential, and sum) and rearrange the result. First, note that

1-P=1-\frac{ce^t}{1+ce^t}=\frac{1+ce^t-ce^t}{1+ce^t}=\frac{1}{1+ce^t}

Now, differentiate to obtain

\frac{dP}{dt}=(\frac{ce^t}{1+ce^t})'=\frac{(ce^t)'(1+ce^t)-(ce^t)(1+ce^t)'}{(1+ce^t)^2}

=\frac{(ce^t)(1+ce^t)-(ce^t)(ce^t)}{(1+ce^t)^2}=\frac{ce^t+ce^{2t}-ce^{2t}}{(1+ce^t)^2}=\frac{ce^t}{(1+ce^t)^2}

To obtain the required form, extract a factor in both the numerator and denominator:

\frac{dP}{dt}=\frac{ce^t}{1+ce^t}\frac{1}{1+ce^t}=P(1-P)

You might be interested in
what is the y-intercept of the equation of the line that is perpendicular to the line y=3/5x+10 and passes through the point (15
ohaa [14]

The slope of the given line is the coefficient of x, 3/5. The slope of the perpendicular line will be the negative reciprocal of that: -1/(3/5) = -5/3.

The point-slope form of the equation for a line of slope m through point (h, k) can be written ...

... y = m(x -h) +k

For your point and the slope found above, this becomes

... y = (-5/3)(x -15) -5

When x=0, this is

... y = (-5/3)(-15) -5 = 20

The y-intercept is 20.

3 0
3 years ago
How many times does 3/8 go into 3/16?
Sunny_sXe [5.5K]

Answer:

1/2

Step-by-step explanation:

(3/16)/(3/8)

(3/16)*8/3

1/2

5 0
3 years ago
Read 2 more answers
Twice the complement of angles A is 40 less than the supplement of angle A. Find the measure of angle A
Serggg [28]
Complement adds to 90
complement of A is 90-A


supplement is adds to 180
supplemetn of A is 180-A

2(90-A) is -40+180-A

2(90-A)=-40+180-A
2(90-A)=140-A
distribute
180-2A=140-A
add 2A to both sides
180=140+A
minus 140 both sides
40=A

A=40 degres
4 0
3 years ago
Read 2 more answers
2 3/4 written as fraction greater than one
sladkih [1.3K]
2 3/4 = 11/4 <=== written as an improper fraction
3 0
3 years ago
Read 2 more answers
5g⁴- 5g³ + 20g² - 20g<br> factor the polynomial
Alina [70]

Answer:

5g⁴- 5g³ + 20g² - 20g

5g(g³-g²+4g-4)

5g(g²(g-1)+4(g-1))

5g(g-1)(g²+4)

7 0
2 years ago
Read 2 more answers
Other questions:
  • Michael is packing his bags for his vacation. He has 5 unique shirts, but only 4 fit in his bag. How many different groups of 4
    15·1 answer
  • Question 3
    5·1 answer
  • Pls help me I’m timed
    12·1 answer
  • kevin borrowed $32,500 to purchase a new car. If the rate on the loan is 6% compounded annually, how much will he pay in total o
    11·1 answer
  • What is the value of -3.25
    8·1 answer
  • PLEASE HELP!!! :( <br>Consider the following figure <br>What is BD? ​
    5·1 answer
  • Just help me. just want a percentage. plsss
    7·1 answer
  • (7, -1) and (21,-5)<br> What is the slope
    5·1 answer
  • A machine is deisgned to fill 16 ounce bottles of shampoo.
    12·2 answers
  • The sum of three number is 14. The sum of twice the first number, 4 times the second number, and 5 times the third number is 41.
    10·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!