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
RideAnS [48]
3 years ago
8

1.12. the time rate of change of an alligator population p in a swamp is proportional to the square of p. the swamp contained a

dozen alligators in 1988, and two dozen in 1998. when will there be four dozen alligators in the swamp? what happens thereafter?

Mathematics
1 answer:
yaroslaw [1]3 years ago
6 0
<h3>Given</h3>

p'(t) = kp²

p(0) = 12; p(10) = 24

<h3>Find</h3>

a) p(t)

b) t such that p(t) = 48

c) the behavior of p(t) after the time of part b

<h3>Solution</h3>

a) The differential equation is separable, so can be solved by separating the variables and integrating.

\displaystyle\frac{d}{dt}p(t)=k\cdot p(t)^{2}\\\\\int{p^{-2}}\,dp=\int{k}\,dt\\\\-p^{-1}=kt+C\\\\p=\frac{-1}{kt+C}

Plugging in the given boundary conditions, we can solve for k and C to find

p(t)=\dfrac{240}{20-t}

b) The population doubles when the time to t=20 is cut in half. The first doubling occurred in 10 years; the second one will occur in half that time, 5 years. There will be 48 alligators in the swamp in 2003.

c) The population doubles again in half the time of the previous doubling, so is predicted to be infinite in 2008.

You might be interested in
2х - 7y = 14<br> Find the x and y- intercepts then graph them.
Anastasy [175]
Nehficnwjaoncncjwjfbcbdkd
Medjjf
4 0
3 years ago
Work out the size of angle x
kompoz [17]

Answer:

x = 117 degrees

Step-by-step explanation:

A triangle has 180 degrees in total.

A straight line is also 180 degrees in total.

180 - 101 = 79

Angles inside the triangle

79 + 38 = 117

180 - 117 = 63

63 degrees is the missing angle

x = 180 - 63

x = 117

6 0
3 years ago
Read 2 more answers
X + 3 = -1 Prove x<br> Need help I need to see work. Don’t understand this problem.
raketka [301]

Answer:

x=-4

Step-by-step explanation:

X needs to be a number that when 3 is added to it, becomes -1. So, adding 3 to -4 gives you -1, therefore, x=-4. Hope this helped!

8 0
3 years ago
darren has 3/4 of a gallon of soil.he needs to plant 5 small plants.if he splits the soil evenly between the plants.how much soi
nika2105 [10]

Number of plants = 5

Amount of soil present for 5 plants = 3/4 gallons

Now here we have to find how much soil will each plant get.

So we have to apply unitary method here to find how much would each plant get the share of soil.

Soil required by 5 plants = 3/4 gallons

Soil required by 1 plant = 3/4 divided by 5 = 3/20 gallons

Answer: Each plant will get 3/20 gallons of soil.

7 0
3 years ago
Read 2 more answers
Сумма пяти последовательных натуральных нечетных чисел равна 9975 Найдите эти числа
iren2701 [21]
Yeah is there a language filter on here ? orr
6 0
3 years ago
Other questions:
  • Mary made 85% of her free-throw attempts. If she missed only six free
    9·1 answer
  • A 4.3 ounce tomato has about 24 calories how many calories are in one ounce
    9·1 answer
  • PLSSS HELP!!!! graph the linear equation x=6
    11·2 answers
  • Question 15(Multiple Choice Worth 1 points)
    15·1 answer
  • Can someone explain how to get this solution?
    11·1 answer
  • -g + 2(3 + g) = -419 + 1)<br> What is the solution
    7·2 answers
  • Divide 80,000 by 100 please help
    14·2 answers
  • Step by step explanation on how to solve (-3 + 8 x 2 -3)
    14·2 answers
  • HELPPPPPPPP!!!! In 1.6, we learned about rational exponents. In a rational exponent, the numerator is the power that the base of
    11·1 answer
  • in Each diagram below right, the 2 numbers on the side of the x that are multiplied together to get the top number of the x but
    12·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!