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Mumz [18]
3 years ago
12

n many population growth problems, there is an upper limit beyond which the population cannot grow. Many scientists agree that t

he earth will not support a population of more than 16 billion. There were 2 billion people on earth at the start of 1925 and 4 billion at the beginning of 1975. If yy is the population, measured in billions, tt years after 1925, an appropriate model is the differential equation
Mathematics
1 answer:
givi [52]3 years ago
3 0

Answer:

\frac{dP}{dt} = rP(1 - \frac{P}{K}) = 0.017P(1 - \frac{P}{16})

Step-by-step explanation:

The logistic function of population growth, that is, the solution of the differential equation is as follows:

P(t) = \frac{KP_{0}e^{rt}}{K + P_{0}(e^{rt} - 1)}

We use this equation to find the value of r.

In this problem, we have that:

K = 16, P_{0} = 2, P(50) = 4

So we find the value of r.

P(t) = \frac{KP_{0}e^{rt}}{K + P_{0}(e^{rt} - 1)}

4 = \frac{16*2e^{50r}}{16 + 2*(e^{50r} - 1)}

4 = \frac{32e^{50r}}{14 + 2e^{50r}}

56 + 8e^{50r} = 32e^{50r}}

24e^{50r} = 56

e^{50r} = 2.33

Applying ln to both sides of the equality

50r = 0.8459

r = 0.017

So

The differential equation is

\frac{dP}{dt} = rP(1 - \frac{P}{K}) = 0.017P(1 - \frac{P}{16})

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2 years ago
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What is the conditional probability that exactly four heads appear when a fair coin is flipped five times
cestrela7 [59]

Answer:

5/32

Step-by-step explanation:

If a coin if flipped five times with four heads, then it has exactly one tail. The number of way to arrange four heads and one tail are as follows:

T H H H H

H T H H H

H H T H H

H H H T H

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Essentially, there are five way because there are five "positions" where the tail could be.

Then, you need to find the total amount of possibilities for flipping a coin five times. Every time you flip it, there are two possibilities- heads and tails. Therefore, for five flips, the total amount of possibilities is

2x2x2x2x2 = 32

You know that

probability= # of desired outcome

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So the probablity is 5/32.

8 0
3 years ago
If x = 8 units and h = 4 units, then what is the area of the triangle shown above?
Luden [163]

Answer:

D-16 square units

Step-by-step explanation:

Area of a triangle- 1/2 x h x base

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5 0
2 years ago
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NEED ANSWERED ASAP WILL REWARD BRAINLIEST
Luda [366]

Answer:

The sum of the first 100 terms is 60400

Step-by-step explanation:

* Lets revise the arithmetic sequence

- There is a constant difference between each two consecutive

  numbers

- Ex:

# 2  ,  5  ,  8  ,  11  ,  ……………………….

# 5  ,  10  ,  15  ,  20  ,  …………………………

# 12  ,  10  ,  8  ,  6  ,  ……………………………

* General term (nth term) of an Arithmetic sequence:

- U1 = a  ,  U2  = a + d  ,  U3  = a + 2d  ,  U4 = a + 3d  ,  U5 = a + 4d

- Un = a + (n – 1)d, where a is the first term , d is the difference

 between each two consecutive terms n is the position of the

 number

- The sum of first n terms of an Arithmetic sequence is calculate from

 Sn = n/2[a + l], where a is the first term and l is the last term

* Now lets solve the problem

- We will use method (1)

- From the table the terms of the sequence are:

 10 , 22 , 34 , 46 , 58 , 82 , 94 , ............., where 10 is the first term

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∵ a1 = 10 and a2 = 22

∵ d = a2 - a1

∴ d = 22 - 10 = 12

- The 100th term means the term of n = 100

∴ a100 = 10 + (100 - 1) 12

∴ a100 = 10 + 99 × 12 = 10 + 1188 = 1198

∴ The 100th term is 1198

- Lets find the sum of the first 100 terms of the sequence

∵ Sn = n/2[a1 + an]

∵ n = 100 , a = 10 , a100 = 1198

∴ S100 = 100/2[10 + 1198] = 50[1208] = 60400

* The sum of the first 100 terms is 60400

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2 years ago
Select the correct answer.
Afina-wow [57]

Answer:

d)\ \frac{81}{m^{7}}

Step-by-step explanation:

(3m^-4)^3(3m^5)

First, simplify (3m^{-4})^3:

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Hope this helps!

5 0
2 years ago
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