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
Denise has 5 hours to spend training for an upcoming race. She completes her training by running full speed the distance of the
Rainbow [258]
<span>To solve this problem, we can use this formula d = rd (distance = rates x time) She runs at a speed of 9 mph and walks at a speed of 3 mph. Her distance running is d = 9tr where tr is the time she spends running Her distance walking is d = 3tw where tw is the time she spends walking The distances are the same so 9tr = 3tw We also know that the total time is 5 hours tr + tw = 5 tr = 5-tw Substitute this value of tr in the first equation 9tr = 3tw 9(5-tw) = 3tw 45-9tw = 3tw 45 = 12tw 3.75= tw Denise will spend 3.75 hours (3 hours, 45 minutes) walking back and 1.25 hours (1 hour, 15 minutes) running.</span>
6 0
2 years ago
Lucas wants to prove that the base angles of any isosceles triangle are
Dmitrij [34]

Answer:

EG so that GF ≈ EF

Step-by-step explanation:

8 0
2 years ago
Read 2 more answers
A rainwater collection tank is shaped like a cylinder with a diameter of 4 ft and height of 6 ft what is its volue
lana [24]
Volume = π×22<span>×6 = </span><span>75.398223686155 feet^3</span>
6 0
3 years ago
Skills Practice: convert the following fractions into decimals. You must show your
Lina20 [59]
ANSWER:
0.25

i attached my work, hope this helps

8 0
2 years ago
If it is January then there are 31 days this month write the inverse of the conditional statement
Vera_Pavlovna [14]
January has 31 days so that mean january is friends with christmas.
6 0
3 years ago
Other questions:
  • Please help me with this problem
    12·2 answers
  • Amina posts three large letters the postage is the same for each letter she pays with a £20 note her change is £14.96 what is th
    14·2 answers
  • Find the first three iterates of the function f(z) = 2z + (3 - 2i) with an initial value of
    14·1 answer
  • 7.3 is what percent of 139?
    14·1 answer
  • What are mind jigglers
    12·1 answer
  • Three friends go apple picking they pick 13 apples on saturday and 14 apples on sunday they share the apples equallyhow many doe
    14·1 answer
  • 30/19 as a mixed number
    10·2 answers
  • Which graph represents the solution set for the system 6x + y &gt; -3 and 2x + y ≤ 4?
    8·2 answers
  • Rosa is at most 29 years old
    7·2 answers
  • I need some help with this plz
    14·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!