The population of rabbits on an island is growing exponentially. In the year 1995, the population of rabbits was 1000, and by 1999 the population had grown to 1800. Predict the population of rabbits in the year 2003, to the nearest whole number.

Answers

Answer 1

Answer:

3,240

Step-by-step explanation:

The computation of the population of rabbits in the year 2003 is shown below:

Given that

In the year 1995, the population of the rabbits was 1000

And, in 1999 the population of the rabbits grown to 1,800

So there is an increase of

= (1800 - 1000) ÷ 1000

= 80%

So for 2003, the population of the rabbits is

= 1800 + (1800 × 0.80)

= 3,240

Answer 2

Given:

The population of rabbits on an island is growing exponentially.

In the year 1995, the population of rabbits was 1000, and by 1999 the population had grown to 1800.

To find:

Expected population of rabbits in the year 2003, to the nearest whole number.

Solution:

The exponential growth model is:

[tex]y=ab^t[/tex]

Where, a is the initial value, b is the growth factor, t is the number of years.

Let y be the population of rabbits t years after 1995.

In the year 1995, the population of rabbits was 1000, it can be written as (0,1000) and by 1999 the population had grown to 1800, it can be written as (4,1800).

For (0,1000),

[tex]1000=ab^0[/tex]

[tex]1000=a(1)[/tex]

[tex]1000=a[/tex]

For (4,1800) and a=1000, we get

[tex]1800=1000b^4[/tex]

[tex]\dfrac{1800}{1000}=b^4[/tex]

[tex]1.8=b^4[/tex]

[tex](1.8)^{\frac{1}{4}}=b[/tex]

[tex]b\approx 1.1583[/tex]

The required exponential model is:

[tex]y=1000(1.1583)^t[/tex]         ...(i)

in year 2003, the number of years since 1995 is 8.

Putting t=8 in (i), we get

[tex]y=1000(1.1583)^8[/tex]

[tex]y=3240.1748[/tex]

[tex]y\approx 3240[/tex]

Therefore, the population of rabbits in the year 2003 is 3240.


Related Questions

HELP DUE IN 10 MINS!

Rounds to nearest foot.

The ladder reaches ?? feet up the wall

Answers

Answer:

Use sine:

x/ 30 = sin 35°x = 30 sin 35°x = 17 ft (rounded)

What is the equation of the line that passes through the point (-6,3) and has a
slope of -1/6?

Answers

Answer:

y = -1/6x + 2

Step-by-step explanation:

Put it in point-slope form:

y - 3 = -1/6(x + 6)

y -3 = -1/6x - 1

y = -1/6x + 2

I need help question in picture

Answers

Area formula of a circle = πr2

π (8.5)2
Area= 226.98

it's is A= pi x r x 2^

diameter is 17 divide by two is the radius

3.14 x 8.5 x 8.5 is 226.865

This list shows the numbers of rocks each member of a rock collection club owns.

5, 18, 26, 11, 3, 20, 9, 12, 24

What is the range of the number of rocks owned by the members?

19
21
23
24

Answers

The answer: 23

Because 26 the largest number minus 3 the smallest number is 23

9. Sara and Yusuf's grandmother gives them money for Christmas every year. They share the money in the
ratio of their ages. This year their grandmother gave them R1 500 together. Sara received R675. They are both younger than 18 years old. Determine how old Sara and Yusuf are.
in​

Answers

Answer:

Sara is 9 years old while Yusuf's is 11 years old

Step-by-step explanation:

The given parameters are;

The ratio Sara and Yusuf share the money they receive = The ratio of their ages

The amount Sara and Yusuf received from their grandmother this year = R1,500

The amount of money Sara receives = R675

Therefore, the amount of money Yusuf receives = R1,500 - R675 = R825

Let 'x', and 'y' represent the ages of Sara and Yusuf

Therefore, the ratio of their ages, x/y = R675/R825) = 9/11

x·11 = y·9

x, and y < 18

When x = 9, y = 11, we  get;

9·11 = 11·9

Therefore a possible solution is Sara's age = x = 9 and a possible solution for Yusuf's age, y = 9

hey could somebody help me please :)

Answers

Answer:

Cut them in smaller shapes then find area

Step-by-step explanation:

Nicole washed 4/10 of a bag of potatoes.She left the rest in a basket outside what amount of potatoes did Nicole leave outside?

Answers

Answer:

6/10 Simplified: 3/5 of a bag

Step-by-step explanation:

One bag= 10/10

She washed 4/10

So, 10/10-4/10=6/10

6/10=3/5

3/5 of a bag

Hope this helped! :)

Stay safe and have a wonderful day/night!!!!!

Please consider rating and giving thanks, if this helped you!

Vanessa throws a tennis ball in the air. The function h(t) = -15t2 + 45t + 10 represents the distance in feet, that the ball is from the ground at any time in seconds, t. What is the maximum height of the ball?

Answers

Answer:

43.75feet

Step-by-step explanation:

Given the height of the tennis ball expressed as;

h(t) = -15t^2 + 45t + 10

At maximum height, the velocity of the ball is zero

v = dh/dt

dh/dt = -30t + 45

Since dh/dt = 0, hence;

0 = -30t + 45

30t = 45

t = 45/30

t = 3/2

t = 1.5secs

Substitute t = 1.5 into the expression given

h(1.5) = -15(1.5)^2 + 45(1.5) + 10

h(1.5) = -15(2.25)+67.5+10

h(1.5) = -33.75+77.5

h(1.5) = 43.75feet

Hence the maximum height of the ball is 43.75feet

Someone help plz make sure it’s right :)

Answers

Answer:

6 m

Step-by-step explanation:

By Pythagoras Theorem:

[tex]x = \sqrt{ {10}^{2} - {8}^{2} } \\ \\ x = \sqrt{100 - 64} \\ \\ x = \sqrt{36} \\ \\ x = 6 \: m[/tex]

Step-by-step explanation:

10² = 8² + x²

x² = 10² - 8²

x² = 36

x = √36

x = 6

There are 12 boys and 13 girls in a class. If the teacher randomly chooses a student's name out of a hat, what is the probability it will be a girl?

◯ 48%
◯ 50%
◯ 52%
◯ 92%

Answers

The probability of selecting a girl is 52%

How to determine the probability?

The given parameters are:

Boy = 12

Girl =13

The probability of selecting a girl is:

P(Girl) = Girl/Total

This gives

P(Girl) = 13/(12 + 13)

Evaluate

P(Girl) = 52%

Hence, the probability it will be a girl is 52%


Read more about probability at:

https://brainly.com/question/251701

#SPJ1

PLSSS HELPPPP I WILLL GIVE YOU BRAINLIEST!!!!!! PLSSS HELPPPP I WILLL GIVE YOU BRAINLIEST!!!!!! PLSSS HELPPPP I WILLL GIVE YOU BRAINLIEST!!!!!! PLSSS HELPPPP I WILLL GIVE YOU BRAINLIEST!!!!!!PLSSS HELPPPP I WILLL GIVE YOU BRAINLIEST!!!!!! PLSSS HELPPPP I WILLL GIVE YOU BRAINLIEST!!!!!! PLSSS HELPPPP I WILLL GIVE YOU BRAINLIEST!!!!!!

Answers

Answer:

268.083

Step-by-step explanation:

volume of a sphere = 4/3 times pi times r^3. 4/3(pi)(4^3) = 268.083

If one side of a triangle is 87 and the other side is 52, what is the measurement of the other side?

Answers

Answer:

87+52=139 180-139 = 41

41 is the measurement of the other side

Step-by-step explanation:

A store purchased jeans for $15 a pair. The store increased the price of the jeans by 65%. One month later, the jeans were on sale for 15 - off the store price. How much would a customer pay for the jeans on sale? Please help

Answers

Answer:

$21.04

Step-by-step explanation:

Steps to take to derive the answer

Determine the price after the price increase of 65%Determine the price after the 15% off

Price after increase increase (100% + increase in price) x purchase price of the jeans

(100% + 65%) x 15

165% x 15

1.65 x $15 = $24.75

Price after the decrease in price = (100% - percentage decrease in price) x price after the 65% increase in price

(100% - 15%) x $24.75

85% x $24.75

0.85 x $24.75 = $21.04

Help ASAP!
553.168 L = mL

Answers

1mL = 0.001 L
so 553168mL

20 POINTS HELP ASAP
determine wether the equation is an identity or not an identity. sin theta/ cos theta

Answers

Answer:

A

Step-by-step explanation:

Instructions: Find the missing length indicated.

Answers

Answer:If you are following a area of a triangle is bxhx1/2 or bxh/2

1,800

Step-by-step explanation:100x36=3,600/2=1,800

Which statement accurately describes the graph 2y=4x+8?


IM IN A TEST HURRY PLEASE!!

Answers

You didn’t give us the statements, send a picture or something.

The statement which describes the given line the best is required.

The correct statement is an increasing line that passes through [tex](0,4)[/tex]

Equation of lines

The given equation is [tex]2y=4x+8[/tex]

Two points of the line are

[tex]x=0[/tex]

[tex]2y=0+8\\\Rightarrow y=4[/tex]

[tex](0,4)[/tex]

[tex]y=0[/tex]

[tex]0=4x+8\\\Rightarrow x=-2[/tex]

[tex](-2,0)[/tex]

The line passes through points [tex](0,4),(-2,0)[/tex]

The slope intercept form of the line is

[tex]y=\dfrac{4x+8}{2}\\\Rightarrow y=2x+4[/tex]

The slope is [tex]2[/tex]

Since, the slope is positive the line is increasing.

Learn more about equation of lines:

https://brainly.com/question/13763238

Which expression is equivalent to

Answers

Answer:

B

Step-by-step explanation:

I need help. Do not post a link to a site!

Find the value of each variable.

Answers

Answer:

the answer is x=45⁰ y=45⁰

may I help you

Find the value or measure. Round answers to the nearest hundredth, as needed.

Answers

Don’t click linkkkkkkkkkkkkk

help please????????????​

Answers

Answer:

1st one is correct ....................

Answer:

x = 8, y = 12

Step-by-step explanation:

Since the triangles are congruent, we know that the parallel sides are equal to each other.

So,

4x - 7 = 3x + 1

4x - 3x = 1 + 7

x = 8

x + y = 20

8 + y =20

y = 20 - 8

y = 12

In triangle ABC, angle C is a right angle. Find the value of the trig function.
Find the cos(A) if c= 15, a=9, b= 12

Answers

Answer:

its a

Step-by-step explanation:

Jimmy is on the driving team at his school the quadratic function graphed on the coordinate plane below represents on of jimmy dives. Where x represent the horizontal distance , in feet that he is from the diving board and y represent his height , in feet above the water level . Explain the meaning of the meaning of x and y intercept in terms of context

Look at the picture :)

Answers

Answer:

X on the graph represents horizontal distance, the x intercept represents when he ends his dive and lands in the water. The x intercept = 8 meaning he is 8 feet away from the diving board when he lands in the water. The y-intercept of y = 13 means the starting point of his dive.

Good luck! :)

Credits: Xin for part A

what is 11 times 1/5

Answers

Answer:

the answer is 2.2

Step-by-step explanation:

I used a calculator

Answer:

2 1/5 I guess

Step-by-step explanation:

If it's wrong then my phone's stu.pid

Work out m and c for the line: y+2x=3

Answers

Answer:

m = - 2, c = 3

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Given

y + 2x = 3 ( subtract 2x from both sides )

y = - 2x + 3 ← in slope- intercept form

with m = - 2 and c = 3

Utilize as propriedades das potências e resolva 2⁴ * 2⁷ * 2⁵​

Answers

Answer:

65536

Step-by-step explanation:

2 elevado a 4 é 16 e 2 elevado a 7 é 128 e 2 elevado a 5 é 32, multiplique-os e você obterá 65536

HELP PLEASE I need it abbreviated !

Answers

Answer:

30 inch²

Step-by-step explanation:

a + b/2 x h

8 + 10/2 X 5 = 30

Divide. (8x2 – 24x + 15) ÷ (2x – 5)

Answers

Answer:

31-24x/2x-5

Step-by-step explanation:

multiply: (16-24x+15)/(2x-5)

calculate: (31-24x)/(2x-5)

write the division as a fraction:  31-24x/2x-5

Find the value or measure. Assume that all segments that appear to be tangent are tangent. Round answers to the nearest tenth, as needed.

Answers

Answer:

23.26

Steps:

AC=√(10²+21²)

AC=√(100+441)

AC=√541

AC≈23.26

Can someone plz help me with this !!!

Answers

Answer:

Yes!

Step-by-step explanation:

The y = -17

The x = 18

y = x-35

-17 does equal 18 - 35

Hope that helps!

Step-by-step explanation: no it dosent i dont think

Other Questions
here's a career question :) (a) Insert a suitable clause below. Remember to use commas.The zoowas very crowded. Create a program which takes two integers as input from the command line. In your code, allocate space for a 2D array dependent on user input. For example, if they enter 30 40 then your program should allocate space using double **. Once the memory is allocated, initialize the data by setting the value at index (i, j) equal to its position a How to Simplify (7^6)^2 I need help with this question please asap I would really appreciate it There are 80 students in a 8th grade, 20% are boys. How many boys are in 8thgrade? What were three major changes to city life at the turn of the 20th century? Please help! Correct answer gets brainliest! Whos someone whos healthy menstlally and physically? Find the surface area ofthe net belowa. 25 square inchesb. 100 square inchesc. 75 square inchesd. 150 square inches How does Hectors rate compare to the fitness challenge rate? Farmers received government assistance for the first time as part of the-A. Fair DealB. New DealC. Marshall PlanD. Truman Doctrine A natural or synthetic substance that when taken into a living body andaffects its functioning or structure is called what? * On Tuesday, Bob brought home an oriental carpet on approval. The price in the store was 9900 Turkish Lira, but Bob was going to pay in dollars. On Tuesday, one dollar was worth 4.5 Turkish Lira. On Wednesday, the Turkish Lira was devalued such that one dollar was now worth 6.5 Turkish Lira. Feeling lucky by this change, Bob then bought the rug on Wednesday, paying the price of 9900 Turkish Lira with dollars at the new rate. To the nearest dollar, how much did he save due to the devaluation? Write 5 Sentences using your vocabulary words in Spanish.acusaradmitirapoyarceloso/achismearchismoso/a gossipycometer un errorcomprensivoconfiar (en)consideradocontar conla culpaQu raro!Qu va!tener celotener la culpala pelea honesto -PLEASE HELP QUESTION IS IN THE PICTURE- is this wrong? Which ordered pairs are solutions to the system of linear equations?y = 2x + 12y - 4x = 2O (0,1)O (1,0)O (2,3)O (-1, - 1).0 (0,0)O (-1,3) _____ is the process for reviewing key roles and determining the readiness levels of potential internal and external candidates to fill these roles. a. Performance management b. War for talent c. Succession planning d. Talent review calibration process e. Talent acquisition what is the slope of the equation y=2/3x-4 what is the slope of the line passing through the points (4,7) and (-2,10)?