About 50 cane toads were introduced into Australia in 1935 to try to control the population of beetles that destroy sugar cane plants. By 2005, there were an estimated 100,000,000 cane toads in Australia. An exponential function that models the number of female cane toads in Australia t years after 1935 is given by f(t)=50(1.23)t .

a. Write a linear function p that models the number of cane toads in Australia t years after 1935. p(t)=___
b. Describe the parameters in the exponential function, , in terms of the context of the problem.
c. Describe the parameters in the linear function, p , in terms of the context of the problem.
Question 4 d. Which model do you think is more appropriate to model the female cane toad population? Use the parameters of the functions to justify your reasoning. Linear or exponential?
Predict the population of female cane toads in Australia in 2000 based on each function. The linear function predicts that there would be _ female cane toads in 2000. The exponential function predicts that there would be ___ female cane toads in 2000.

Answers

Answer 1

The linear function predicts that there would be 92857146 female cane toads in 2000 while the exponential function predicts that there would be 34898137 female cane toads in 2000.

Part A: The linear model of the number of cane toads

From the question, we have the following points

(t, f(t)) = (0,50) and (70, 100000000)

The linear function is then calculated as:

f(t) = [f(t2) - f(t1)]/[t2 - t1](t - t1) + f(t1)

This gives

f(t) = [100000000 - 50]/[70 - 0](t - 0) + 50

Evaluate

f(t) = 1428570.71t + 50

Hence, the linear function is f(t) = 1428570.71t + 50

Part B: The parameters in the exponential function

The exponential function is given as:

f(t) = 50(1.23)^t

So, the parameters are:

50 represents the initial value1.23 represents the ratet represents the number of years from 1935f(t) represents the number of cane toad in year t

Part C: The parameters in the linear function

The exponential function is calculated as:

f(t) = 1428570.71t + 50

So, the parameters are:

50 represents the initial value1428570.71 represents the ratet represents the number of years from 1935f(t) represents the number of cane toad in year t

Part D: The appropriate model

When the population of an entity is being model, it is best to use the exponential model, because the populations would grow exponentially for some time, and then stop growing at some point

Hence, the more appropriate model is the exponential model.

Part E: The number of female cane toads in 2000

The year 2000 is 65 years from 1935.

So, we have:

t = 65

For the exponential model, we have:

f(t) = 50(1.23)^t

The equation becomes

f(65) = 50(1.23)^65

Evaluate

f(65) = 34898137

For the linear function, we have:

f(t) = 1428570.71t + 50

The equation becomes

f(65) = 1428570.71 * 65 + 50

Evaluate

f(65) = 92857146

This means that. there would be 34898137 female cane toads in 2000 according to the exponential function.

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Related Questions

What’s the answer for this…

Solve for p

2p + 3 > 2 (p – 3)

Answers

Answer:

2p+3>2(p−3)

Use the distributive property to multiply 2 by p−3.

2p+3>2p−6

Subtract 2p from both sides.

2p+3−2p>−6

Combine 2p and −2p to get 0.

-3>6

This is true for any p.

p∈R

Step-by-step explanation:

Hope this helps! :)

Answer:

C. No solution

Step-by-step explanation:

Sove for p;

2p + 3 > 2 (p – 3)

First: distribute 2 (p – 3):

2 (p – 3)

2(p) + 2(-3)

2p - 6

Now add it back to your original problem:

2p + 3 > 2p - 6

Subtract 3 from both sides of the equation:

2p + 3 > 2p - 6

- 3 - 3

2p > 2p -9

Subtract 2p from both sides of the equation:

2p > 2p -9

-2p -2p

0 > -9

Therefore, this inequality has no solution, because we could solve for p.

Hope this helps!

solve for d . 8d-6d=10

Answers

Simplifying

8d + -6d = 10

Combine like terms: 8d + -6d = 2d

2d = 10

Solving

2d = 10

Solving for variable 'd'.

Move all terms containing d to the left, all other terms to the right.

Divide each side by '2'.

d = 5

Simplifying

d = 5

What is the meaning of the sum?

Answers

Answer:

the sum is the total amount resulting from the addition of two or more numbers, amounts, or items.

A group of students formed a circle during a game. The circumference of the circle was about 50.24 feet, and the diameter of the circle was 16 feet. Which expression best represents the value of π?

Answers

A group of students formed a circle during a game. The circumference of the circle was about 50.24 feet, and the diameter of the circle was 16 feet. The required expression for value of π is: 3.14

What is diameter of circle?

A circle is a form made up of all points on a plane that are at a specific distance from the centre point. In other words, it is the path a moving point in a plane takes to travel around a curve while maintaining a constant distance from another point.

Given that,

The circumference of the circle was about 50.24 feet,

And the diameter of the circle was 16 feet

We have to determine,

Which expression best represents the value of π.

According to the question,

Circumference of the circle = 50.24 feet

Diameter f the circle = 16 feet

Then,

Circumference of the circle = π × d

Circumference of the circle = 50.24 feet

Therefore,

50.24 = π × d

or. π × 16 = 50.24

or, π = 3.14

Hence, The required expression for value of π is: 3.14

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#SPJ1

Please help i will give brainliest

Answers

Answer:

c or a one of the 2

Step-by-step explanation:

What is the value of x in the given triangle, in inches?

Answers

Hence, the value of sin 90° is 1.
So, the correct option is (D).

Miss Chang ordered a pizza to share with some Grade 8 students. Miss Chang

gave Michael some slices of pizza. Miss Chang gave Amy twice as many slices of

pizza as Michael. Miss Chang gave Mr. Au three times the sum of what she gave

to Michael and Amy. Miss Chang gave 60 slices of pizza to Michael, Amy and Mr.

Au in total. How many slices of pizza Miss Chang give to each person?

Answers

Michael: x
Amy: 2x
Mr. Au: 3(2x+x)
x+2x+3(2x+x)=60
x+2x+3(3x)=60
x+2x+9x=60
12x=60
x=5
Michael: 5 slices
Amy: 2(x)
2(5)=10 slices
Mr. Au: 3(2x+x)
3(10+5)=45 slices

What is the area of the figure?

A figure can be broken into 2 rectangles. One rectangle has a base of 6.2 inches and height of 8 inches. The other rectangle has a base of 10.2 inches and height of 3 inches.
42.4 square inches
80.2 square inches
92.8 square inches
101.6 square inches

Answers

Answer:

80.2

Step-by-step explanation:

Answer:80.2

Step-by-step explanation:

i did the test so yeh edg 2023

PLEASE PLEASE PLEASE HELP ME WITH THIS QUICK QUESTION!!!!!!!!!

Answers

Answer:

y intercept: 4, x-intercept: None

Step-by-step explanation:

Took the test and got it right

I am struggling with both questions please help.

Answers

Step-by-step explanation:

xbc = 55

because corresponding angle of parallel lines are equal

BXC = 70

because triangle XBC is Isosceles triangle

angle B = angle C

B = C = 55

so angle

BXC = 180 - 55 - 55

BXC = 180 - 110

BXC = 70

The number of bacteria on a microscope slide doubles every hour . There are initially 4 bacteria present . Create an explicit function fto model the growth after n hours .

Answers

Answer:

I think a possible equation can be; f(n) = 4(2)ⁿ

f(n) = a * bˣ

Where;

f(n) = the function of f for every n value

a = Initial value (in this case it would be 4)

b = Rate of change (in this case it would be 2, since the bacteria doubles)

x = exponent (in this case it would be n)

So our final equation would be:

f(n) = 4(2)ⁿ

Hope this helps!

find the m of arc AB, round to nearest tenth.

Answers

Answer:

80°

Step-by-step explanation:

AB and AC are chords.

Chords AB and AC are at a distance of 2 units from the center of the circle.

-> Chord AB = Chord AC

[tex]\implies m(\widehat {AB})=m(\widehat {AC})[/tex]...(1)

(Equal chords intercept equal arcs)

[tex]m(\widehat {AB})+m(\widehat {AC})+m(\widehat {BC})=360\degree[/tex]

(By arc sum property of a circle)

[tex]\implies m(\widehat {AB})+m(\widehat {AB})+200\degree=360\degree[/tex]

(From equation 1)

[tex]\implies 2m(\widehat {AB})=360\degree-200\degree[/tex]

[tex]\implies 2m(\widehat {AB})=160\degree[/tex]

[tex]\implies m(\widehat {AB})=\frac{160\degree}{2}[/tex]

[tex]\implies \huge{\orange{m(\widehat {AB})={80\degree}}}[/tex]

How would I solve this and what’s the answer ?

Answers

To solve this you just move the letters and numbers around until you get a different equation that is the same as the original equation.

You can also rule out the last two answers because they don’t have all the values.

P = pie

s=2prh can be written as s/2ph=r if we divide s by 2ph because we need to isolate r because all the answers have r isolated.

So the answer would be b s/2ph=r

Sorry that’s really badly worded and confusing, but I hope it helps.

Which equation can be used to represent the statement? Half of a number minus Severn is one and five tenths.

Answers

1/2x-7=1 5/10
Or 1 1/2

help me answer this pls

Answers

p = -4 and q = -6

hope it helps...!!!

. A bag has 16 marbles in it: 6 red, 4 blue, 3 yellow, and 3 green. A marble is drawn and put back, and
then another marble is drawn. What is the probability that a blue marble was drawn followed by a
yellow marble?

Answers

Answer:

64%

Step-by-step explanation:

The function
f
(
t
)
=
310
(
1.025
)
7
t
f(t)=310(1.025)
7t
represents the change in a quantity over t weeks. What does the constant 1.025 reveal about the rate of change of the quantity

Answers

Answer: The function is growing exponentially at a rate of 2.5% every day.

Step-by-step explanation:

How Do I Do Goldbach’s Conjecture.

Answers

I dk bc I don’t understand what you mean

An airplane covers 900 miles in first 30 minutes and 3040 miles in next 2 hours. What is the speed of the airplane in the first 30 minutes

Answers

Answer:

hi how do you do I actually don't know sorry very much

What is the equation, in slope-intercept form, of the line that contains the points (1, -4) and (2, 1)?

X Y
1 -4
2 1
A. y = 5x - 9
B. y = -5x + 9
C. y = -9x + 5
D. y = 9x - 5

Answers

Step-by-step explanation:

please mark me as brainlest

Answer:

A Y= 5x-9

Step-by-step explanation:

URGENT SOLVE 7 8 and 9 THAMK YOU SO MUCHHH

Answers

Answer:

7) a

8) b

9) d

Step-by-step explanation:

HELPPPPPPPPPP!!! pls show work

Answers

Answer:

Step-by-step explanation:

67 becaue you divide all the numbers together then add then multiply then subtract divide that number and you get 67

The product of two consecutive integers is 272. which quadratic equation can be used to find x, the smaller number? x2 1 = 272 x2 − 1 = 272 x2 x − 272 = 0 x2 x 272 = 0

Answers

An equation is formed of two equal expressions. The quadratic equation that can be used to find x, the smaller number is x²+x-272.

What is an equation?

An equation is formed when two equal expressions are equated together with the help of an equal sign '='.

Let the first number be x.

Now since the two numbers are consecutive numbers the other number will be (x+1). Also, it is mentioned in the problem that the product of the two numbers is 272. Therefore, the equation that can represent the product will be,

[tex]x \times (x+1) = 272\\\\x^2 + x =272\\\\x^2 + x -272 = 0[/tex]

Thus, the quadratic equation that can be used to find x, the smaller number is x²+x-272.

Learn more about Equation:

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Answer:

c. x2 + x − 272 = 0

Step-by-step explanation:

PLEASE SOLVE!! DUE RIGHT NOW!!! WILL MARK BRAINLIEST IF ANSWERED AND CORRECT!!!!!

Answers

Step-by-step explanation:

a) The measure of angle 7 is also 47 degrees. We know this because angle 5 and angle 7 are vertical angles and vertical angles are always equal.

b and c) Since we know that a straight line has an angle of 180 degrees and that the sum of angle 5 and angle 6 will add to this, we can use that to find the value of x like this:

[tex]47+2x-5=180\\47-5+2x=180\\42+2x=180\\42-42+2x=180-42\\2x=138\\\frac{2x}{2} =\frac{138}{2} \\x=69[/tex]

Which products result in a difference of squares or a perfect square trinomial? check all that apply. (5x 3)(5x – 3) (7x 4)(7x 4) (2x 1)(x 2) (4x – 6)(x 8) (x – 9)(x – 9) (–3x – 6)(–3x 6)

Answers

(7x + 4)(7x + 4) and (x – 9)(x – 9) are Perfect square trinomial. (5x + 3)(5x – 3) and (–3x – 6)(–3x + 6) shows the Difference of squares.

What is a perfect square?

A perfect square is a number system that can be expressed as the

square of a given number from the same system.

The following are the answers

(5x + 3)(5x – 3) Difference of squares

(7x + 4)(7x + 4) is a Perfect square trinomial

(2x + 1)(x + 2) has Neither a difference of squares nor a perfect square trinomial.

(4x – 6)(x + 8) has Neither a difference of squares nor a perfect square trinomial.

(x – 9)(x – 9) is Perfect square trinomial

(–3x – 6)(–3x + 6) = [tex](-3x)^2- ( -6)^2[/tex] Difference of squares.

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Answer:

A. B, E, F

Step-by-step explanation:

If a point is randomly selected from the rectangular area of the graph, what is the probability that it will be in the blue region? Round answer to the nearest whole percent.
A) 49%
B) 59%
C) 69%
D) 79%

Answers

Answer:

D) 79%

Step-by-step explanation:

I had this question on USATestprep and got it right.

A bag Contains five blue marbles two green marbles and three yellow marbles what is the probability of Choosing one Green marble and a yellow marble with replacement what does this mean

Answers

Answer:

3/50.

Step-by-step explanation:

There are 10 marbles in the bag.

Probability( a green marble) = 2/10 = 1/5.

Now we replace the green marble in the bag so it contains 10 marbles again.

Probabilty(a yellow marble) = 3/10.

So Probability(Choosing a green then a red with repeacemen)

= 1/5 * 3/10

= 3/50.

Williana’s mother wants to buy a glass tabletop for their dining room table. The tabletop is shaped like a hexagon with sides measuring 27. 75 inches. If the glass costs $0. 06 per square inch, how much will she spend on the glass table top?

$

Answers

The total amount that Williana's mother would spend to buy the glass table top is $120.04.

What is the total cost of the glass table top?

The first step is to determine the area of the glass table top.

Area of a hexagon = [(3√3)/2] x a²

a = side length

2.598 x 27.75² = 2000.68 in²

Cost of the table top = 2000.68 in² x 0.06 = $120.04

To learn more about hexagonal prisms, please check: https://brainly.com/question/27242498

Find the volume of the rectangular prism with the following dimensions: L=1/2 w=1
h=3/4

Answers

Answer:

3/8 cubic units

Step-by-step explanation:

The volume of a rectangular prism is given by the formula ...

V = LWH

Using the given dimensions, we find the volume to be ...

V = (1/2)(1)(3/4) = 3/8 . . . . cubic units

Find the 4th term in the sequence
with the following definition:

a1 = 0
a2 = -6
an = 2(an-1-3)

Answers

The sequence an = 2(an-1 - 3) is a recursive sequence

The 4th term of the sequence is -42

How to determine the 4th term?

The given parameters are:

a1 = 0

a2 = -6

an = 2(an-1 - 3)

Start by calculating a3 using:

a3 = 2(a2 - 3)

This gives

a3 = 2 * (-6 - 3)

a3 = -18

Calculate a4 using:

a4 = 2(a3 - 3)

This gives

a4 = 2 * (-18 - 3)

a4 = -42

Hence, the 4th term of the sequence is -42