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
grandymaker [24]
2 years ago
5

1. The number of rabbits on an island is increasing exponentially.

Mathematics
1 answer:
Zina [86]2 years ago
5 0

Answer:

<em>There are approximately 114 rabbits in the year 10</em>

Step-by-step explanation:

<u>Exponential Growth </u>

The natural growth of some magnitudes can be modeled by the equation:

P=P_o(1+r)^t

Where P is the actual amount of the magnitude, Po is its initial amount, r is the growth rate and t is the time.

We are given two measurements of the population of rabbits on an island.

In year 1, there are 50 rabbits. This is the point (1,50)

In year 5, there are 72 rabbits. This is the point (5,72)

Substituting in the general model, we have:

50=P_o(1+r)^1

50=P_o(1+r)\qquad\qquad[1]

72=P_o(1+r)^5\qquad\qquad[2]

Dividing [2] by [1]:

\displaystyle \frac{72}{50}=(1+r)^{5-1}=(1+r)^{4}

Solving for r:

\displaystyle r=\sqrt[4]{\frac{72}{50}}-1

Calculating:

r=0.095445

From [1], solve for Po:

\displaystyle P_o=\frac{72}{(1+r)^5}

\displaystyle P_o=\frac{72}{(1.095445)^5}

P_o=45.64355

The model can be written now as:

P=45.64355(1.095445)^t

In year t=10, the population of rabbits is:

P=45.64355(1.095445)^{10}

P = 113.6

P\approx 114

There are approximately 114 rabbits in the year 10

You might be interested in
How far will a skier travel in 2 1/2 minutes? Explain how you figured it out
Kay [80]

3600 meters 60 seconds would be 1440 traveled

and 1440 + 1440 + 720= <u>3600</u>

Hope this helps :)

8 0
3 years ago
1. {-7, -3, -9/11, √9, 18/5}
Sunny_sXe [5.5K]

Answer:

In response to the above problems, the predecessors have made many efforts. ese include collaborative computing between terminal devices and cloud servers [6][7][8], model compression and parameter pruning [9][10][11][12], or customized mobile implementation [13][14][15]. Despite all these efforts made by the predecessors, on the premise of ensuring the accuracy of the model required by the user, the service latency is minimized, and the user's hardware configuration and system status can be sensed to implement automatic model pruning and partition. ...

Step-by-step explanation:

I hope it will help you

7 0
2 years ago
Read 2 more answers
Please Help!<br> The following is an isosceles trapezoid, find m &lt; J
ra1l [238]

Answer:

<em>The measure of angle J is 44°</em>

Step-by-step explanation:

<u>Isosceles Trapezoid</u>

The isosceles trapezoid has its non-parallel sides of the same length, thus the angles they form with their respective parallel sides are congruent.

It means: Angle J is congruent with angle K and angle M is congruent with angle L

The sum of angles in a trapezoid is 180*(4-2)=360°

Thus:

m\angle J+m\angle K+m \angle M+m\angle L = 360^\circ

7x+2+7x+2+25x-14+25x-14=360

Joining like terms:

64x-24=360

Adding 24:

64x=384

Dividing by 64:

x=6°

Thus:

m\angle J = 7*6+2=44^\circ

m\angle M = 25*6-14=136^\circ

The measure of angle J is 44°

3 0
3 years ago
Please help!!! (5 points)
Fofino [41]

Answer:

0.75

Step-by-step explanation:

3 0
3 years ago
The sum of three integers is 12
Liula [17]

The three integers are 5,17 and -10

Step-by-step explanation:

Let x, y and z be three integers then

x+y+z=12 \ \ \Eqn\ 1

'The sum of the first and second integers exceeds the third by 32'

x+y=z+32\ \ \ \ Eqn\ 2

The third integer is 15  less than the first.

z=x-15\ \ \ \ Eqn\ 3

From Eqn 2:

x+y=z + 32\\x+y-z=32

Subtracting Eqn 1 from eqn 2

x+y-z-(x+y+z)=32-12\\x+y-z-x-y-z=20\\-2z=20

Dividing both sides by -2

\frac{-2z}{-2}=\frac{20}{-2}\\z=-10

Putting z=-10 in Eqn 3

z=x-15\\-10=x-15\\x=15-10\\x=5

Putting x=5 and z=-10 in Eqn 1

x+y+z=12\\5+y-10=12\\y-5=12\\y=12+5\\y=17\\

Hence,

The three integers are 5,17 and -10

Keywords: Linear Equations, Variables

Learn more about linear equations at:

  • brainly.com/question/13219835
  • brainly.com/question/1836777

#LearnwithBrainly

3 0
3 years ago
Read 2 more answers
Other questions:
  • Let's say we have a circle with a radius of 17 inches. What is the circumference of this circle in inches? Round your answer to
    14·1 answer
  • Please help and thank you
    11·2 answers
  • PLZ HELP QUESTION 3 20 POINTS!!!!
    6·1 answer
  • Please help meee, I’m having trouble in math. I solved the answer but got none of these.
    13·1 answer
  • What's the area of this rectangle?
    15·1 answer
  • Simplify this expression 3(2x-6)+x.
    9·2 answers
  • Find the size of the angle a.<br><br>Diagram not drawn accurately​
    15·1 answer
  • HELP WHATS THIS ANSWER?? WILL MARK BRAINLIEST
    8·1 answer
  • Michelle's bird feeder holds 4/5 of a cup of birdseed. Michelle is filling the bird feeder with a scoop that holds 2/5 of a cup.
    12·2 answers
  • According to the Fundamental Theorem of Algebra a 5th degree function has how many zeros?
    10·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!