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
ahrayia [7]
3 years ago
15

The population of Collin County, which follows the exponential growth model, increased from 491,675 in 2000 to 782,341 in 2010.

Find the exponential growth rate, k.
Mathematics
1 answer:
Luden [163]3 years ago
6 0

Answer:

p=ak^t

p1=491272*k^0

p2=782341*k^10

782341/491272 = k^10

k=1.047629

growth rate is 4.7629%

2012: predicted population is 491272*1.047629^12=858,642 people

1245863=491272*1.047629^t

1.047629^k=2.5363599

ln both sides is k ln 1.0476=ln 2.5363

t=20.000 years.

Rule of 72 would say 72/4.76 or 15.12 years for doubling

14.90 years

2017 predicted is 491272*1.0476^17 or 1083552, or more than actual, so the rate of growth is slowing down.

You might be interested in
Find the slope of the line below. Enter your answer as a fraction or decimal. Use a slash mark (/) as the fraction bar if necess
Llana [10]

Answer:

1/4

Step-by-step explanation:

We can use the slope formula to find the slope

m = (y2-y1)/(x2-x1)

    = (2-0)/(4 - -4)

    = (2-0)/( 4+4)

    = ( 2/8)

    = 1/4

3 0
3 years ago
Read 2 more answers
12What mistake did the student make when solvingtheir two-step equation?(a)b) If correctly solved what should the value of be?
mixas84 [53]

Given the equation:

\frac{x}{6}+3=-18

(a) You can identify that the student applied the Subtraction Property of Equality by subtraction 3 from both sides of the equation:

\frac{x}{6}+3-(3)=-18-(3)

However, the student made a mistake when adding the numbers on the right side.

Since you have two numbers with the same sign on the right side of the equation, you must add them, not subtract them and use the same sign in the result. Then, the steps to add them are:

- Add their Absolute values (their values without the negative sign).

- Write the sum with the negative sign.

Then:

\frac{x}{6}=-21

(b) The correct procedure is:

1. Apply the Subtraction Property of Equality by subtracting 3 from both sides (as you did in the previous part):

\begin{gathered} \frac{x}{6}+3-(3)=-18-(3) \\  \\ \frac{x}{6}=-21 \end{gathered}

2. Apply the Multiplication Property of Equality by multiplying both sides of the equation by 6:

\begin{gathered} (6)(\frac{x}{6})=(-21)(6) \\  \\ x=-126 \end{gathered}

Hence, the answers are:

(a) The student made a mistake by adding the numbers -18 and -3:

-18-3=-15\text{ (False)}

(b) The value of "x" should be:

x=-126

4 0
1 year ago
Which of the following describes muckrakers.
Evgesh-ka [11]

Answer:

I think it's A

Step-by-step explanation:

6 0
3 years ago
What is the absolute value of 1? I’ll mark you brainlist pls help
Nonamiya [84]

Answer:

1

Step-by-step explanation:

3 0
3 years ago
Read 2 more answers
An open box with a square base is constructed so that it has a volume of 64in^3. The base needs to be made out of a material tha
Ivahew [28]

The volume of a box is the amount of space in the box

The dimensions that minimize the cost of the box is 4 in by 4 in  by 4 in

<h3>How to determine the dimensions that minimize the cost</h3>

The dimensions of the box are:

Width = x

Depth = y

So, the volume (V) is:

V = x^2y

The volume is given as 64 cubic inches.

So, we have:

x^2y = 64

Make y the subject

y = \frac{64}{x^2}

The surface area of the box is calculated as:

A =x^2 + 4xy

The cost is:

C = 2x^2 + 4xy --- the base is twice as expensive as the sides

Substitute y = \frac{64}{x^2}

C = 2x^2 + 4x * \frac{64}{x^2}

C =2x^2 +  \frac{256}{x}

Differentiate

C' =4x -  \frac{256}{x^2}

Set to 0

4x -  \frac{256}{x^2} = 0

Multiply through by x^2

4x^3 -  256= 0

Divide through by 4

x^3 -  64= 0

Add 64 to both sides

x^3 =  64

Take the cube roots of both sides

x = 4

Recall that:

y = \frac{64}{x^2}

So, we have:

y = \frac{64}{4^2}

y = 4

Hence, the dimensions that minimize the cost of the box is 4 in by 4 in  by 4 in

Read more about volume at:

brainly.com/question/1972490

4 0
2 years ago
Other questions:
  • Please help me on this thank you
    12·1 answer
  • The Pythagorean Theorem what is this????????
    7·1 answer
  • 75% of 48 explain the process too!
    9·1 answer
  • Graph the equation on the coordinate plane.
    14·1 answer
  • The height of a triangle is 4 in. greater than twice its base. The area of the triangle is no more than 168 in.2. Which inequali
    6·2 answers
  • Find the area of the trapezoid with bases of 10 in and 14 in, and a height of 5 in.
    8·1 answer
  • John, Karl, and Marcus each have a different favorite subject: math, English, and science. Each also has a different favorite co
    10·1 answer
  • 2.7x -9 = x +7.5 need the answer can't find solution.
    8·2 answers
  • Prove that: [1 + 1/tan²theta] [1 + 1/cot² thata] = 1/(sin²theta - sin⁴theta]
    11·1 answer
  • Lauren says the two expressions 3x+4(2x+5) and 6x +5x+5 are equivalent
    13·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!