The following functions give the populations of four towns with time tt in years.
(i) P=600(1.12)^t
(ii) P=1,000(1.03)^t
(iii) P=200(1.08)^t
(iv) P=900(0.90)^t
Which town has the largest percent growth rate? What is the percent growth rate?

Answers

Answer 1

Solution :

Transforming given equations :

[tex]1)\ P = 600( 1 + \dfrac{12}{100})^t\\\\2)\ P = 1000( 1 + \dfrac{3}{100})^t\\\\3)\ P = 200( 1 + \dfrac{8}{100})^t\\\\4)\ P = 900( 1 - \dfrac{10}{100})^t[/tex]

From above equations we can see that equation 1) has largest percentage growth rate and the percent growth rate is 12% .

Hence, this is the required solution.

Answer 2

Answer: (i), 12%

Step-by-step explanation:

Given

The Population of four towns is given

(i) [tex]P=600(1.12)^t[/tex] i.e.

[tex]\Rightarrow P=600(1+0.12)^t\\\Rightarrow P=600(1+12\%)^t[/tex]

rate=12%

(ii) [tex]P=1000(1.03)^t[/tex]

[tex]\Rightarrow P=1000(1+0.03)^t\\\Rightarrow P=1000(1+3\%)^t[/tex]

rate=3%

(iii) [tex]P=200(1.08)^t[/tex]

[tex]\Rightarrow P=300(1+0.08)^t\\\Rightarrow P=300(1+8\%)^t[/tex]

rate=8%

(iv) [tex]P=900(0.90)^t[/tex]

[tex]\Rightarrow P=900(1-0.10)^t\\\Rightarrow P=900(1-10\%)^t[/tex]

rate=10% fall

So, the largest growth rate is for town (i)  i.e. 12%


Related Questions

In ΔFGH, the measure of ∠H=90°, FH = 8, OF = 17, and HG = 15. What ratio represents the sine of ∠G?

Answers

Answer:

[tex]\sin(G) = \frac{8}{17}[/tex]

Step-by-step explanation:

Given

[tex]\angle H = 90^o[/tex]

[tex]FH = 8[/tex]

[tex]GF = 17[/tex]

[tex]HG = 15[/tex]

See attachment for illustration

Required

The ratio of [tex]\sin(G)[/tex]

[tex]\sin(G)[/tex] is calculated as:

[tex]\sin(G) = \frac{Opposite}{Hypotenuse}[/tex]

From the attachment, we have:

[tex]\sin(G) = \frac{FH}{GF}[/tex]

This gives:

[tex]\sin(G) = \frac{8}{17}[/tex]

What percent of l0.2 gram of 32 mg

Answers

The percent of 10.2 gram of 32 mg is gotten to be; 31.875%

How to find the percentage?

When we are trying to find the percentage with the expressions "if" and "of", we will use the formula;

is/of *100%

Now, we want to find the percentage of 10.2 gram of 32 mg. Thus, the percentage is expressed as;

10.2/32 * 100% = 31.875%

Thus, the percent of l0.2 gram of 32 mg is gotten to be 31.875%

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Can you help me in question 30?!

Answers

Answer:   24

Step-by-step explanation:

Answer:

24

Step-by-step explanation:

Volume is length times width times height so you just have to multiply 3 by 4 by 2 to get 24.

And then next time we will come back and

Answers

There isn’t really a question

Which graph shows the solution set of the inequality 2.9(x+8) <26.1?
O
+++
-10
-5
0
5
10
-10
-5
0
5
10
O
-10
-5
0
5
5
10
-10
-5
5
5
10

Answers

9514 1404 393

Answer:

  D

Step-by-step explanation:

The inequality symbol is < (not ≤), which means the end point of the graph will be an open circle.

After dividing by the coefficient of x, you have an inequality of the form ...

  x +( ) < ( )

which means the solution will be left of the (open circle) end point of the graph. Only one graph has that form.

__

If you actually work through the numbers, you get ...

  x +8 < 9 . . . . . . divide both sides by 2.9

  x < 1 . . . . . . . . . subtract 8 from both sides

Which graph represents the solution set for the inequality 1xs 18?
2
+++
0 1 2
3 4 5 6 7 8 9 10
>
+++
0 6 12 18 24 30 36 42 48 54 60
+
0 1 2 3 4 5 6 7 8 9 10
0 6 12 18 24 30 36 42 48 54 60

Answers

9514 1404 393

Answer:

  D

Step-by-step explanation:

Multiplying the inequality by 2 will eliminate the fraction and give you ...

  x ≤ 36

The "or equal to" part of the symbol means the end dot will be solid. The "less than" part of the symbol means the graph is shaded to the left of the end dot, which is at x=36. This description matches the graph shown below.

find the area for brainlest

Answers

Answer:

A = 30 units²

Step-by-step explanation:

The area (A) of a triangle is calculated as

A = [tex]\frac{1}{2}[/tex] bh ( b is the base and h the perpendicular height )

Here b = 12 and h = 5 , then

A = [tex]\frac{1}{2}[/tex] × 12 × 5 = 6 × 5 = 30 units²

What are the roots of the equation x2 + 16x + 73 = 0 in simplest a + bi form?

Answers

Answer:

-8+2i and -8+2i

Step-by-step explanation:

here simply we'll use general formula

x= (-b +or - √ b^2-4ac)/2a

find the y-intercept for the parabola
defined by this same equation:
y = 2x2 – 8x + 5

Answers

Answer:

y=5

y int

x=0

y=2(0)^2-8(0)+5

y=5

note everything multiplied by 0 is 0

The time it takes to build a house (T), varies directly with the floor area (A), and inversely with the number of workers (W). What is the equation that models this situation?

Answers

Answer:

T = k * (A/W)

Step-by-step explanation:

In a recent survey, 75% of the community favored building a police substation in their neighborhood. If 14 citizen are chosen at random, find the probability that exactly 8 of them favor the building of the police substation.
.

Answers

Answer:

/ROB.UX ME 1,000,000,000

Step-by-step explanation:

Answer:

.073398

Step-by-step explanation:

It's easiest to use a binomial distribution here

We have...

14C8*.75⁸*(1-.75)⁶= .073398

Two containers designed to hold water are side by side, both in the shape of a cylinder. Container A has a diameter of 16 feet and a height of 19 feet. Container B has a diameter of 20 feet and a height of 15 feet. Container A is full of water and the water is pumped into Container B until Container A is empty.

To the nearest tenth, what is the percent of Container B that is empty after the pumping is complete?

Answers

18.9% is the answer

Step-by-step explanation:

volume of a cylinder = πd²/4 x h

where d is diameter and h is height of cylinder.

thus

vol of A is

[tex]vol \: of \: a \: = \pi \times \frac{ {d}^{2} }{4} \times h \\ = \pi \times \frac{ {16}^{2} }{4} \times 19 \\ = \pi \times 4 \times 16 \times 19 \\ = 3818.24[/tex]

and

[tex]vol \: of \: b = \pi \times \frac{ {20}^{2} }{4} \times 15 \\ = \pi \times 5 \times 20 \times 15 \\ = 4710[/tex]

difference in vol of a and b is

[tex]diff \: = vol \: of \: b \: - vol \: of \: a \\ = 4710 - 3818.24 \\ = 891.76[/tex]

this volume will remain empty after container A is pumped into container B.

this volume as a percentage of total volume of B is

[tex]\% = \frac{diff \: vol}{total \: vol} \times 100 \\ = \frac{891.76}{4710} \times 100 \\ = 18.9\%[/tex]

A person drives a car between the two places x and y. On his outward journey he consumes 8 km per liter of petrol, on his return journey he covers 12 km per liter. Find the average of his mileage assuming the distance between the two places to be 100​

Answers

:/ im sorry but i needa get my points i dnt kno the answer tho srry

Are (2, 5) and (5, 2) the same location? Why or why not?

Answers

Answer:

They are not in the same location

Step-by-step explanation:

Well because we have x axis and y axis, x always has to go first. In (2, 5) 2 is first and has to start from the x axis and 5 is the y axis. And the (5,2) is the opposite and the places would be in totally different places on the coordinate plane.

Answer: No

Step-by-step explanation: The order of coordinates for a given point is very important. For example, (2, 5) and (5, 2) represent two very different points on a coordinate system, as shown in the picture below.

A given point, such as (2, 5), is often reffered to as

an ordered pair because the order of coordinates is very important.

Choose the definition for the function. please help me

Answers

9514 1404 393

Answer:

  A

Step-by-step explanation:

It is usually sufficient to look at one section of the graph to answer a question like this. Often the best choice is the section that has a solid dot at the end of the curve. Here, that is the right section.

The left end of the right section is at x=-2, so that part of the function is defined for x ≥ -2. The line to the right has a positive slope, so the coefficient of x will be positive.

Only one answer choice has a positive x-coefficient for x ≥ -2.

  [tex]\textbf{A. }\begin{cases}-x-2&\text{if }x<-2\\x+4&\text{if }x\ge-2\end{cases}[/tex]

Answer:

Step-by-step explanation:

This graph is made up of two different, separate line segments.  In other words, it comes in two pieces which can be described as a pair of linear functions.

We call this a "piecewise linear" function.  Choice A is the best one.

3y=150, what is the value of y-2​

Answers

Answer:

y = 48

Step-by-step explanation:

Start with the given 3y = 150.

Solve this for y by dividing both sides by 3:  y = 50

Then y - 2 = 50 - 2, or

        y    =    48

The value of y-2 is 48,

What is an equation?

Two expressions connected by an equal sign makes an equation.

Given is an equation, 3y = 150

Solving for y,

3y = 150

y = 150 / 3

y = 50

therefore, y-2 = 50-2

= 48

Hence, the value of y-2 is 48,

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If can someone help me.

Answers

9514 1404 393

Answer:

  Tim is correct. 5/8 > 1/2

Step-by-step explanation:

By taking 5/8 of the lasagna, Tim will be taking more than half (4/8) of it. No remaining share can be larger. Any remaining share will be 3/8 or less, so will be smaller than a 5/8 share.

Tim's 5/8 share is the largest.

my question is in the document

Answers

The document isn’t loading for me

please answer !!! quickly thank you! ​

Answers

Answer:

B) this line has zero slope.

Step-by-step explanation:

it doesn't increase or decrease. it is a constant; zero

Answer:

This line has zero slope.

Step-by-step explanation:

The slope of the line doesn't change it just stays straight.

The weights (in ounces) of 28 tomatoes are listed below. 1.1 1.6 1.8 1.9 2.0 2.3 2.3 2.5 2.5 2.5 2.5 2.6 2.6 2.6 2.8 2.9 2.9 3.0 3.1 3.1 3.1 3.3 3.4 3.5 3.5 3.6 3.9 4.9 What is the five number summary?​

Answers

Answer:

2.6 2.6 2.8 2.9 2.9

Step-by-step explanation:

used median for the five numbers.

Help troll or report Help plsssss

Answers

Answer:

11. (a) 3/4+1/2=5/4

   (b) 4/5= 8/10 , 16/20

12. 8 children don't like choc ice cream

Step-by-step explanation:

11. 3/4 +2/4=5/4(change 1/2 by making it the same as the one next to it)

12. 3/5 of 20 = 12

     20-12=8

The parent function f(x)=x^3 is transformed to g(x)=(x-1)^3+4. Which graph represents function g?

Answers

The answer is B. Look at this

Which graph represents the function f(x) = –x2 + 5?

Answers

Answer:

Step-by-step explanation:

The graph of f(x) = –x^2 + 5 is that of an upside-down parabola with vertex (0, 5) and x-intercepts (-√5, 0) and (+√5, 0).  Plot the vertex (0, 5) and then draw a smooth curve through it and through the x-intercepts.

The function f(x) = -x2+5 is thus represented by the quadratic functions in the first graph.

what is quadratic functions ?

A quadratic function has the formula f(x) = ax2 + bx + c, with a, b, and c being integers and a not equal to zero.  Parabolas can have openings that are upward or downward, different "widths" or "steepnesses," but they all share the same fundamental "U" shape.

here calculation

The function provided is f(x) =  -x2+5

.... (1) (1)

We must locate the function's graph.

The quadratic function's vertex form is f(x)= a(x-h)2 + k.... (2)

When we compare (1) and (2), we obtain

h=0 , k=5

It denotes that the function's vertex is (0,5).

The values list is

x           y

-2            1

-1            4

0            5

1            4

2           1

Place all ordered pairings on a coordinate plane, and then use a free-hand curve to link them.

The function f(x) = -x2+5 is thus represented by the quadratic functions in the first graph.

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A spinner is divided into 4 equal sections numbered 1 through 4. It is spun twice, and the numbers from each spin are added.

What is the probability that the sum is less than 6?

Answers

Answer:

4equal to plus 5 eul is to be 9

CALCULATORS COST $125.00 FOR 25 CALCULATORS. WHAT IS THE COST PER CALCULATOR?​

Answers

Answer: $5 per calculator

Step-by-step explanation: divide 125 and 25

Answer:

5$

Step-by-step explanation:

Given:

25 calculators cost 125.00

So:

_______ DIvide the cost of calculators by the number of calculators, and we get 5$

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``````````````````````````````````

Answers

Answer:

~~~~~~~~~~~~~~~~~~~~~~~~~.~~~~~~~~~~~~~~~~~~~~~~~~~

Step-by-step explanation:

Type the correct answer in each box. Use numerals instead of words. if necessary, use / for the fraction bar(s).
Find the sum. Write your answer in simplest form.

Answers

Answer:

[tex]\frac{11}{12} - \frac{1}{3} = \frac{7}{12}[/tex]

Step-by-step explanation:

Given

See attachment for question

Required

Solve

We have:

[tex]\frac{11}{12} - \frac{1}{3}[/tex]

Take LCM and solve

[tex]\frac{11}{12} - \frac{1}{3} = \frac{11 - 4}{12}[/tex]

[tex]\frac{11}{12} - \frac{1}{3} = \frac{7}{12}[/tex]

Answer:

1

Type the correct answer in each box. Use numerals instead of words. If necessary, use / for the fraction bar(s).

Find the sum. Write your answer in simplest form.

Step-by-step explanation:

A 16 ft ladder leans against the side of a house. The bottom of the ladder is 9 ft away from the side of the house. Find x, the angle of elevation of the ladder. Round your answer to the nearest tenth of a degree. (plz help listing BRAINLIST)​

Answers

Answer:

55.8

Step-by-step explanation:

cos(x)=9/16

x=55.8

The angle of elevation of the ladder is approximately 60.5 degrees.

To find the angle of elevation (x) of the ladder, we can use trigonometry. The ladder, the side of the house, and the ground form a right triangle. The length of the ladder is the hypotenuse of the right triangle, and the distance from the bottom of the ladder to the house is one of the legs.

Using the tangent function:

tan(x) = opposite/adjacent

tan(x) = 16 ft / 9 ft

Now, solve for x:

x = arctan(16/9)

Using a calculator, we find

x ≈ 60.5 degrees

So, the angle of elevation of the ladder is approximately 60.5 degrees.

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A is set of positive multiples of 5 less than 23

Answers

9514 1404 393

Answer:

  {5, 10, 15, 20}

Step-by-step explanation:

Multiples of 5 are of the form 5n, where n is an integer. The ones of interest will satisfy ...

  0 < 5n < 23

  0 < n < 4.6

That is, the multiples of 5 we want are for values of n that are 1 through 4. The set is ...

  5 × {1, 2, 3, 4} = {5, 10, 15, 20}

A universal set U consists of elements. If sets​ A, B, and C are proper subsets of U and ​n(U)​, ​n(A ​B)​n(A ​C)​n(B ​C)​, ​n(A B ​C)​, and​ n(A B ​C)​, determine each of the following.

a. n(AUB)
b. n(A'UC)
c. n(AnB)'

Answers

Answer:

[tex]n(A\ u\ B) = 10[/tex]

[tex]n(A'\ u\ C) = 10[/tex]

[tex]n(A\ n\ B)' = 6[/tex]

Step-by-step explanation:

Given

[tex]n(U) = 12[/tex]

[tex]n(A\ n\ B) =n(A\ n\ C) = n(B\ n\ C) =6[/tex]

[tex]n(A\ n\ B\ n\ C)=4[/tex]

[tex]n(A\ u\ B\ u\ C)=10[/tex]

Required

Solve a, b and c

There are several ways to solve this; the best is by using Venn diagram (see attachment for diagram)

Solving (a):

[tex]n(A\ u\ B)[/tex]

This is calculated as:

[tex]n(A\ u\ B) = n(A) + n(B) - n(A\ n\ B)[/tex]

From the attachment

[tex]n(A) = 0+2+4+2 = 8[/tex]

[tex]n(B) = 0+2+4+2 = 8[/tex]

[tex]n(A\ n\ B) = 4 +2 = 6[/tex]

So:

[tex]n(A\ u\ B) = 8 + 8 - 6[/tex]

[tex]n(A\ u\ B) = 10[/tex]

Solving (b):

[tex]n(A'\ u\ C)[/tex]

This is calculated as:

[tex]n(A'\ u\ C) = n(A') + n(C) -n(A'\ n\ C)[/tex]

From the attachment

[tex]n(A) = n(U) - n(A) = 12 - 8 = 4[/tex]

[tex]n(C) = 0+2+4+2 = 8[/tex]

[tex]n(A'\ n\ C) = 2[/tex]

So:

[tex]n(A'\ u\ C) = 4 + 8 - 2[/tex]

[tex]n(A'\ u\ C) = 10[/tex]

Solving (c):

[tex]n(A\ n\ B)'[/tex]

This is calculated as:

[tex]n(A\ n\ B)' = n(U) - n(A\ n\ B)[/tex]

[tex]n(A\ n\ B)' = 12- 6[/tex]

[tex]n(A\ n\ B)' = 6[/tex]

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