The initial population of the town was estimated to be 12,500 in 2005. The population has increased by about 5.4% per year since 2005.

Formulate the equation that gives the population, A(x) , of the town x years since 2005. If necessary, round your answer to the nearest thousandth.

A(x)=__(_)^x

Answers

Answer 1

Answer:

[tex]A(x) = 12500(1.054)^x[/tex]

Step-by-step explanation:

Exponential equation for population growth:

Considering a constant growth rate, the population, in x years after 2005, is given by:

[tex]A(x) = A(0)(1 + r)^x[/tex]

In which A(0) is the population in 2005 and r is the growth rate, as a decimal.

The initial population of the town was estimated to be 12,500 in 2005.

This means that [tex]A(0) = 12500[/tex]

The population has increased by about 5.4% per year since 2005.

This means that [tex]r = 0.054[/tex]

So

[tex]A(x) = A(0)(1 + r)^x[/tex]

[tex]A(x) = 12500(1 + 0.054)^x[/tex]

[tex]A(x) = 12500(1.054)^x[/tex]


Related Questions

There are 40 children in a classroom and n of them do not wear spectacles. (4)/(5) of the boys and (2)/(3) of the girls wear spectacles. Express the number of boys who wear spectacles in terms of n.

Answers

9514 1404 393

Answer:

  b = 80 -6n . . . . boys who wear spectacles

Step-by-step explanation:

We know the ratio of boys who wear spectacles to those who don't is ...

  (4/5) : (1 -4/5) = 4 : 1

If we let b represent the number of boys who wear spectacles, then the number who don't is b/4. Then total number of boys is then b +b/4 = 5b/4. The number of girls in the classroom is this number less than 40.

Let's define a few groups:

boys who wear spectacles: bboys who do not wear spectacles: b/4girls who wear spectacles: (2/3)(40 -5b/4)girls who do not wear spectacles (1/3)(40 -5b/4)

Then the total of children who do not wear spectacles is ...

  n = b/4 +(1/3)(40 -5b/4)

  12n = 3b +(160 -5b) = 160 -2b . . . . multiply by 12

  2b = 160 -12n . . . . . . . . . . . . . add 2b-12n

  b = 80 -6n . . . . the desired relation, b = boys who wear spectacles

_____

Additional comment

The only values of n that make sense in this context are {8, 10, 12}, corresponding to {0, 15, 30} total girls and {40, 25, 10} total boys.

Suppose f(x)=x^2. What is the graph of g(x)=1/2f(x)?

Answers

9514 1404 393

Answer:

  see attached

Step-by-step explanation:

The graph of g(x) is a vertically scaled version of the graph of f(x). The scale factor is 1/2, so vertical height at a given value of x is 1/2 what it is for f(x). This will make the graph appear shorter and fatter than for f(x).

The graph of g(x) is attached.

A bottling machine fills soda bottles with an average of 12.000 ounces of soda. The standard deviation is 0.002 ounces. If the design specification for the fill weight of the bottles is 12.000 ounces plus or minus 0.015 ounces, calculate the process capability index of the machine. Group of answer choices Less than or equal to 1 More than 4 More than 2 but less than or equal to 3 More than 1 but less than or equal to 2

Answers

Answer:

the process capability index of the machine is 2.5

Option c) [More than 2 but less than or equal to 3] is the correct answer

Step-by-step explanation:

Given the data in the question;

process average ( x') = 12.000 ounces

standard deviation σ = 0.002 ounces

the design specification for the fill weight of the bottles is 12.000 ounces plus or minus 0.015 ounces.

so

Upper specification Limit USL = 12.000 + 0.015 = 12.015 ounces

Lower specification Limit LSL = 12.000 - 0.015 = 11.985 ounces

the process capability index of the machine will be;

Cp = ( process average - Lower specification Limit ) /  3σ

so we substitute

Cp = ( 12 - 11.985 ) / ( 3 × 0.002 )

Cp = 0.015 / 0.006

Cp = 2.5

Therefore, the process capability index of the machine is 2.5

Option c) [More than 2 but less than or equal to 3] is the correct answer

What is the solution to this equation?
6
O A. x = 18
O B. x= -2
O c. x= -18
O D. X= 21

Answers

Answer:

O C. x = -18

Step-by-step explanation:

x/-3 = 6

x = denominator multiplied by quotient.

x = -3 x 6

x = -18

Lisa reads an equal number of pages of a book every week. The graph below shows the number of pages of the book left to read, y, after x weeks:

A graph titled Lisas Book Reading shows Number of Weeks on the x-axis and Number of Pages Left on the y-axis. The scale on the x-axis shows numbers from 0 to 6 at increments of 1, and the scale on the y-axis shows numbers from 0 to 350 at increments of 50. A straight line joins the ordered pairs 0, 250 and 1, 200 and 2, 150 and 3, 100 and 4, 50 and 5, 0.

Which equation best models the relationship between x and y?

y = −50x + 250
y = −5x + 50
y = −50x + 350
y = −5x + 250

Answers

9514 1404 393

Answer:

  (a)  y = −50x + 250

Step-by-step explanation:

In case you don't realize that the graph starts at 250 and decreases by 50 for each increase of 1 in x, you can see if any of the equations match the given points. The only one that does is the first one:

  y = -50x +250

Answer:

(a)  y = −50x + 250

Step-by-step explanation:

HELPP PLEASEEEEEEEEEEEEEEEEEEEEEE

The sum of 6 and 12 divided by 9.

Answers

6 + 12 = 18
18/9 = 2

The answer is 2

Hope this helps
6+(12/9)=7.33333333333

Find the slope and then an equation for each line.

Answers

the slope for 1 is 3/9 or 1/3 so the equation can be y-0=1/3(x-0)
and for 2 the slope is -2/-8 or 1/4 and the equation is y-0=1/4(x-0)

What is the product?
(-2d^2+5)(5d^2-6s)

Answers

Answer:

= -10d^4 + 12d^2s + 25d^2 - 30s

Left on together, the cold and hot water faucets of a certain bathtub take 4 minutes to fill the tub. If it takes the hot water faucet minutes to fill the tub by itself, how long will it take the cold water faucet to fill the tub on its own?
Do not do any rounding.

Answers

Answer:

[tex]Cold = \frac{1}{6}\ mins[/tex]

Step-by-step explanation:

The correct given parameters are:

[tex]Both = \frac{1}{4}\ mins[/tex]

[tex]Hot = \frac{1}{12}\ mins[/tex]

Required

Time taken by the cold water faucet

We have:

[tex]Cold + Hot = Both[/tex]

Make Cold the subject

[tex]Cold = Both -Hot[/tex]

So, we have:

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

Take LCM

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

[tex]Cold = \frac{2}{12}[/tex]

Divide by 2

[tex]Cold = \frac{1}{6}[/tex]

find c.round to the nearest tenth

Answers

Answer:

we need a picture...

Step-by-step explanation:

I need help finding the answer to this question on edge.

Answers

Answer:

6

Step-by-step explanation:

We need to evaluate :-

[tex]\rm\implies \displaystyle\rm\sum^4_n (-1)^n (3n + 2 ) [/tex]

Here the [tex]\Sigma[/tex] is the sum operator . And here we need to find the sum from n = 1 to n = 4 . We can write it as ,

[tex]\rm\implies (-1)^1 ( 3*1 +2) + (-1)^2 ( 3*2+2) + (-1)^3(3*3+2) + (-1)^4(3*4+2) [/tex]

Now we know that for odd powers of -1 , we get -1 and for even powers we get 1 . Therefore ,

[tex]\rm\implies -1 ( 3 + 2 ) + 1 (6+2)+-1(9+2)+1(12+2)[/tex]

Now add the terms inside the brackets and then multiply it with the number outside the bracket . We will get ,

[tex]\rm\implies -1 * 5 + 1 * 8 + -1*11 + 1*14 \\\\\rm\implies -5 + 8 - 11 + 14 \\\\\rm\implies\boxed{\quad 6 \quad}[/tex]

Hence the required answer is 6.

People's movements between places is called

Answers

Answer:

The three answers I can think of are migration, immigration, and emigration.

Step-by-step explanation:

Hope this helps!

spatial interaction. The movement ( e.g. of people, goods, information ) between different places; an indication of interdependence between different geographic locations or areas

need assistance with this, thank you ​

Answers

Answer:

B. 1✓3 in.

Search It ok

I see the answer :)

I almost got the problem but the problem was the rounding. I believe I rounded right but it is still incorrect. Can someone please help me on the rounding portion of the question? Thank you for your help!!!

Answers

Answer: The answer that I got for z was 0.111575, which when you round it to the hundredths place would be 0.11

What is the answer to this

Answers

Answer:

y = -1.5x - 1

Step-by-step explanation:

We can use the general equation of y = mx + c to form our linear equation as seen on this graph.

Choosing two points on the graph (I will choose 0,-1 and 2,-4) we can find the gradient, m, as the distance between these points

[tex]\frac{Rise}{Run} = \frac{(-1)-(-4)}{(0)-(2)} = \frac{3}{-2} =-1.5[/tex]

We can find the c value by seeing where the graph cuts through the y-axis

This point is -1

Therefore our equation is y = -1.5x - 1

Alternatively, you could write it as [tex]y= -\frac{3}{2} x - 1[/tex]

Answer:

y = -1.5x - 1

PLEASE HELP AND BE CORRECT BEFORE ANSWERING

Answers

9514 1404 393

Answer:

  3

Step-by-step explanation:

The length of A'B' is 3 units.

The length of AB is 1 unit.

The scale factor is A'B'/AB = 3/1 = 3.

An oil tanker spills oil that spreads in a circular pattern whose radius increases at a rate of 15 ft/min. Let A be the area of the circle and r be the radius of the circle. How fast is the area increasing when the radius is 30 feet

Answers

Answer:

[tex]2827.4 \dfrac{ft}{s}[/tex]

Step-by-step explanation:

[tex] A = \pi r^2 [/tex]

[tex] \dfrac{dA}{dt} = 2 \pi r \dfrac{dr}{dt} [/tex]

[tex] \dfrac{dA}{dt} = 2 \times \pi \times 30~ft \times 15 \dfrac{ft}{s} [/tex]

[tex] \dfrac{dA}{dt} = 2827.4 \dfrac{ft}{s} [/tex]

help me with my work pls

Answers

Answer:

-75/4

Step-by-step explanation:

75 x 100 = 7500

4 x 100 = 400

Determine whether or not the given procedure results in a binomial distribution. If not, identify which condition is not met. Surveying 26 people to determine which brand of ice cream is their favorite.
A. Yes
B. No
There are more than two possible outcomes on each trial of the experiment. The experiment does not consist of n identical trials. The trials are dependent.

Answers

Answer:

The answer is "No, There are more than two possible outcomes on each trial of the experiment ".

Step-by-step explanation:

When various ice cream products are known. This might surpass 2 brands or more. Thus the number of different results varies considerably.

BINOMIAL DISTRIBUTION:

An investigation with a set set of individual tests, each only with two possible results.

Four conditions are met by the binomial experiment

The set of indicators is fixed.Each attempt is autonomous.2 potential results exist only.In each and every test, the probability of each outcome remains unchanged.

hellppp................

Answers

Answer:

[tex]B)[/tex]

[tex](-1,1)(-3,3)\\\frac{3-1}{-3+1} =-1\\1=1+b\\b=0\\y=-x[/tex]

OAmayOHopeO

Simplify 3/4 + 5/8 over 3/4 - 1/2

Answers

Answer:

11/2

Step-by-step explanation:

[tex]\frac{\frac{3}{4} + \frac{5}{8} }{\frac{3}{4} - \frac{1}{2} }[/tex]

= 3/4 + 5/8 = 11/8 (take LCM)

3/4 - 1/2 = 1/4 (take LCM)

11/8 ÷ 1 /4

= 11/8 x 4

= 11/2

Answered by Gauthmath

write your answer in simplest radical form​

Answers

9514 1404 393

Answer:

  f = 3 units

Step-by-step explanation:

The ratios of side lengths in this 30°-60°-90° triangle are ...

  1 : √3 : 2

So, the ratio of interest is ...

  1 : √3 = √3 : f

We can see that the numbers in the second ratio are √3 times the numbers in the first ratio, so

  f = √3 × √3 = 3

  f = 3 units

g Find an equation of the line with slope m that passes through the given point. Put the answer in slope-intercept form. (-4, 8), undefined slope Hint: Any line parallel to Y axis has undefined slope.

Answers

Answer:

The equation is x + 4 = 0.

Step-by-step explanation:

Point (-4 , 8)

A line parallel to the Y axis has slope is infinite.

The equation of line is

[tex]y - y' = m (x-x')\\\\y - 8 =\frac{1}{0}(x+4)\\\\x + 4 = 0[/tex]

−3 1​/2 ÷ 1 1/4
khan academy
answer in simplified proper fraction
or
simplified improper fraction

Answers

Answer:

Step-by-step explanation:

Change the mixed numbers to improper fractions.

Umm.. Hi there! Can someone please help me out with this? (only for those who know the answer)

Bcoz I really need this rn :(


DUEEEE AFTERRR LUNCHH! :(:(:(:(


If your answer is NONSENSE it will be deleted as soon as possible!

But if your answer is CORRECT, HELPFUL, HAS AN EXPLANATION, I'll chose your answer as the BRAINLIEST ANSWER!

Answers

Answer:

The Exterior Angle of triangle LDR is angle d. The Remote Interior Angles are a and b.

The Exterior Angle of triangle PDR is angle 4. The Remote Interior Angles are angles 1 and 2

Explanation:

Interior angles are the angles that are inside the shape. The remote interior angles would be the 2 angles away from the exterior angle.

The exterior angle is the angle, made by the side of the shape and a line drawn out from an adjacent side.

I hope this helps!

Answer:

In LDR

Exterior = d Interior = a, b

In PDR

Exterior = 4Interior = 1, 2

Exterior angle of a triangle is formed when one side of the triangle is extended .

Interior remote angles the angles in the triangle that do not lie on the extended side.

. Mildred bought an old
necklace and pair of earrings
while at an antique show. If
the cost of the jewelry is ]
and tax is 7%, which of the
following equations could be
used to find the total cost of
the jewelry?
a. .07 + ]
b. J +.07 x)
C. (.07x)) + ]
d. 7) + ]

Answers

Answer:

j * .07 +j

Step-by-step explanation:

The tax on the jewelry is J* .07

Add the tax to the cost of the jewelry to get the total cost

j * .07 +j

Use the functions below to complete Parts 1 and 2.

f(x)= |x| g(x)= |x+2| - 3

Part 1: Graph f(x) and g(x) on the grid below. Label each graph.

HINT: Making a table of values for each function may help you to graph them.

Part 2: describe how the graph of g(x) relates to the graph of its parent function, f(x).

HINT: Think about how f(x) was shifted to get g(x).

Answers

9514 1404 393

Answer:

  1. see below

  2. g(x) is f(x) translated left 2 and down 3

Step-by-step explanation:

1. The graphs are attached. F(x) is in red; g(x) is in blue.

__

2. The graph of g(x) = f(x -h) +k is the parent function translated by (h, k). Here we have (h, k) = (-2, -3), so g(x) is f(x) translated left 2 and down 3.

The number 0 is a critical point of the autonomous differential equation dx/dt = 7xn, where n is a positive integer. For what values of n is 0 asymptotically stable? Semi-stable? Unstable?

Answers

Answer:

a) 0 is stable when n = odd

b) 0 is semi-stable when n = even

c) 0 is unstable when n is odd

Step-by-step explanation:

Th differential equation for this question

dx/dt = x^n

n = positive integer

a) value of n where 0 is stable

0 is stable when x^n is replaced with -x^n

because considering n to be an odd number

-x^n > 0 when x < 0    while -x^n < 0 when x > 0

∴ In this scenerio we can conclude that 0 is stable when  n = odd number

b) Value of n where 0 is Semi-stable

assuming n is an even number

x^n > 0  for all the values of x

c) Value of n where 0 is unstable

lets assume n is odd

when n < 0,  xⁿ < 0

when n > 0,  xⁿ > 0

i.e. 0 is asymptotically unstable when n is an odd number

Which of these shapes have the same area?

Answers

Answer:

wheres the picture?

Step-by-step explanation:

Solve for x.
7(x+2) = 6(x+5)
O x=-44
O X=-16
O x= 44
O x= 16

Answers

Answer:

x = 16

Step-by-step explanation:

7(x + 2) = 6(x + 5)

First, to start solving this problem, we have to distribute the "7" to the "x + 2" in the parenthesis and the "6" to the "x + 5" in the parenthesis.

7x + 14 = 6x + 30

Next, let's subtract "6x" from both sides of this equation!

x + 14 = 30

Now, we have to subtract "14" from both sides of the equation.

x = 16

Lastly! Let's make sure our "x=" equation is correct by inputting our value into the "x" values.

7(16 + 2) = 6(16 + 5)

7(18) = 6(21)

126 = 126

Since our equations equal each other we know that our x-value is correct!

Hope this Helps! :)

Have any questions? Ask below in the comments and I will try my best to answer.

-SGO

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