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
anzhelika [568]
3 years ago
7

In 1859, 24 rabbits were released into the wild in Australia, where they had no natural predators. Their population grew exponen

tially, doubling every 6 months.
a. Determine P(t), the function that gives the population at time t, and the differential equation describing the population growth.
b. After how many years, rounded to one digit after the decimal point, did the rabbit population reach 1,000,000?
c. Determine the rate of population change, in rabbits/year, midway through the third year. (Warning: t is not 3.5, just like the year midway through the 21st century is not 2150.) Round the final answer to 2 digits after the decimal point.
Mathematics
1 answer:
Mashcka [7]3 years ago
4 0

Answer:

a) P' = P

   P(t) = 24e^{0.693t} where t is step of 6 months

b) 7.7 years

c)1064.67 rabbits/year

Step-by-step explanation:

The differential equation describing the population growth is

\frac{dP}{dt} = P

Where t is the range of 6 months, or half of a year.

P(t) would have the form of

P(t) = P_0e^{kt}

where P_0 = 24 is the initial population

After 6 month (t = 1), the population is doubled to 48

P(1) = 24e^k = 48

e^k = 2

k = ln(2) = 0.693

Therefore P(t) = 24e^{0.693t}

where t is step of 6 months

b. We can solve for t to get how long it takes to get to a population of 1,000,000:

24e^{0.693t} = 1000000

e^{0.693t} = 1000000 / 24 = 41667

0.693t = ln(41667) = 10.64

t = 10.64 / 0.693 = 15.35

So it would take 15.35 * 0.5 = 7.7 years to reach 1000000

c. P' = P_0ke^{kt}

We need to resolve for k if t is in the range of 1 year. In half of a year (t = 0.5), the population is 48

24e^{0.5k) = 48

0.5k = ln2 = 0.693

k = 1.386

Therefore, P' = 1.386*24e^{1.386t}

At the mid of the 3rd year, where t = 2.5, we can calculate P'

P' = 1.386*24e^{1.386*2.5} = 1064.67 rabbits/year

You might be interested in
Can y'all help me with my math problem please
Greeley [361]

Answer:

it is C

Step-by-step explanation:

3 0
2 years ago
Read 2 more answers
How do you find the quotient of 2 fractions? <br> E.g, 3/5 and 9/10.
liq [111]

Answer:

by dividing the fractions

4 0
2 years ago
Read 2 more answers
Which is the better buy? a 12-pack of Pepsi for $3.50 or a 6 pack for $1.80
xxMikexx [17]

Answer:

1.80

Step-by-step explanation:

it very useful to understand very well

4 0
2 years ago
Read 2 more answers
there are 18 boys and 12 girl in math class. what is the ratio of girls to total students. A. 18:30 B. 12:30 C. 30:12 D. 30:18 2
zmey [24]

Answer:

1.  B

2. B and C

3.C

4.B the answer is 238 but i guess the rounded

Step-by-step explanation:

3 0
3 years ago
Read 2 more answers
Ppppplllssss heeellppppppppppppllllpllklgfgtfchgrrdgvcfyrf
zubka84 [21]

Answer:

Equation: 3x - 11 = 85

Solution: x = 32

Step-by-step explanation:

3x - 11 = 85

You will have to do the opposite to the equation shown on the screen.

3x = 96 (85 + 11)

x = 32 (96 / 3)

3 0
1 year ago
Other questions:
  • The diameter of the circle is 24m.Tim incorrectly says that the circumference of the circle is about 37.68 m.What is the circumf
    8·1 answer
  • There were n signers of the Declaration of Independence. The youngest was Edward Rutledge, who was x years old. x is 25% of 104.
    14·1 answer
  • Which is traveling faster, a car whose velocity vector is 201 + 25), or a car whose velocity vector is 30i, assuming that the un
    7·1 answer
  • A new car sells for $30,000. The value of the car decreases by 16% annually. After how many years will the car be worth less tha
    6·1 answer
  • What is the value of n?
    6·1 answer
  • Hey can anyone help me was this math problem<br> 2+2?
    13·2 answers
  • Write an expression to represent the number of pencils Cindy has.
    8·1 answer
  • Solve for a.
    14·2 answers
  • If f(x)=1/9x-2, what is f^-1(x)?​
    9·1 answer
  • 1. In a board game, students draw a number, do not replace it, and then draw a second number. Determine the probability of each
    10·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!