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
Helen [10]
2 years ago
7

Task 2 a. Do some research and find a city that has experienced population growth. Determine its population on January 1st of a

certain year. Write an exponential function to represent the city’s population, y, based on the number of years that pass, x after a period of exponential growth. Describe the variables and numbers that you used in your equation. b. Find another city whose population starts larger than the city in part (a), but that during this same time experienced population decline. Determine its population for January 1st of the same year you picked for part (a). Write an exponential function to represent the city’s population, y, based on the number of years that pass, x after a period of population decline. Describe the variables and numbers that you used in your equation. c. Explain the similarities and differences between your equations in (a) and (b). d. During what year will the population of city (a) first exceed that of city (b)? Show all of your work and explain your steps. e. During what year will the population of city (a) be at least twice the size of the population of city (b)? Show all of your work and explain your steps.
Mathematics
1 answer:
Galina-37 [17]2 years ago
3 0

Exponential functions are functions defined by y = ab^x, where a represents the initial value, and b represents the rate

<h3>The equation of a city that has experienced a population growth</h3>

The initial population of the city is 10000, and the growth rate of the population is 4%.

So, the exponential equation is:

y = 10000 * 1.04^x

<h3>The equation of a city that has experienced a population decline</h3>

The initial population of the city is 12000, and the decay rate of the population is 3%.

So, the exponential equation is:

y = 12000* 0.97^x

<h3>The similarities in the equations</h3>

The similarity in both equations is that, they both represent exponential function.

<h3>The year the population of city A exceeds B</h3>

In (a) and (b), we have:

y = 10000 * 1.04^x ---- city A

y = 12000* 0.97^x --- city B

When city A exceeds city B, we have the following inequality

10000 * 1.04^x > 12000 * 0.97^x

Divide both sides by 10000

1.04^x > 1.2 * 0.97^x

Divide both sides by 0.97^x

(\frac{1.04}{0.97})^x > 1.2

1.07^x > 1.2

Take the natural logarithm of both sides

\ln(1.07)^x > \ln(1.2)

This gives

x\ln(1.07) > \ln(1.2)

Solve for x

x > \frac{\ln(1.2)}{\ln(1.07)}

x > 2.69

This means that, the population of city A will exceed city B after 3 years

<h3>The year the population of city A will be at least twice of city B</h3>

In (a) and (b), we have:

y = 10000 * 1.04^x ---- city A

y = 12000* 0.97^x --- city B

When city A is at least twice city B, we have the following inequality

10000 * 1.04^x \ge 2 * 12000 * 0.97^x

10000 * 1.04^x \ge 24000 * 0.97^x

Divide both sides by 10000

1.04^x \ge 2.4 * 0.97^x

Divide both sides by 0.97^x

(\frac{1.04}{ 0.97})^x \ge 2.4

1.07^x \ge 2.4

Take the natural logarithm of both sides

\ln(1.07)^x \ge \ln(2.4)

This gives

x\ln(1.07) \ge \ln(2.4)

Solve for x

x\ge \frac{\ln(2.4)}{\ln(1.07) }

x\ge 12.9

This means that, the population of city A will be at least twice city B after 13 years

Read more about exponential functions at:

brainly.com/question/11464095

You might be interested in
–5x+8y= 10<br> 7x-2y= -14
Lostsunrise [7]

Answer:

x=2,y=0

(You did not provide enough information for me to know what to do with said equations, so I'm assuming it was System of Equations.)

7 0
2 years ago
Identify the Vertex: x^2 - 12x + 44
nikklg [1K]

The vertex of the given quadratic polynomial function is (6, 8)

A quadratic polynomial function is the one which can be represented in the form ax² + bx + c = y where a, b and c are coefficients and x, and y are independent and dependent variables respectively. A parabola is formed when the quadratic polynomial is plotted on graph. The x coordinate of the vertex can be found using formula (-b/2a) and y coordinate can be found by putting the value of x in the equation.

Given polynomial function x² - 12x + 44

Now, x = (-b/2a)

x = (12/2)

=> x = 6

Now, y = 6² - 12×6 + 44

y = 36 - 72 + 44

=> y = 8

Therefore, Vertex = (6, 8)

Learn more about Vertex of quadratic polynomial at:

brainly.com/question/15385707

#SPJ9

3 0
1 year ago
A typical television newscast has three cameras. The center camera directly faces the news anchors desk. The other two cameras a
Mnenie [13.5K]
<span>150 degrees. Let's assume the center camera is pointed to at an angle of 0 degrees. Since it has a coverage of 60 degrees, then it will cover the angles from -30 to +30 degrees. Now we'll continue to use the +/- 30 degree coverage for the other two cameras. The second camera is aimed at 45 degrees, so it's range of coverage is 15 degrees to 75 degrees (45 +/- 30). Notice that the range from 15 degrees to 30 degrees is covered by 2 cameras. Now the 3rd camera is pointed at -45 degrees, so its coverage is from -15 degrees to -75 degrees. It also has an overlap with the 1st camera from -15 to -30 degrees. The total coverage of all three cameras ranges from -75 degrees to 75 degrees. That means that an arc of 150 degrees in total is covered by all three cameras.</span>
7 0
3 years ago
A space shuttle orbits Earth at a speed of 21,000 km/hr. How far will it travel in 5 hours?
tresset_1 [31]
<span>21,000*5
since it travels 21,000 per hour and there is five hours. it's just simple substitution.
105,000 is the correct answer.</span>
7 0
3 years ago
Read 2 more answers
Find All numbers whose absolute value is 2
Elanso [62]

Answer:

Step-by-step explanation:

Absolute Value. Absolute value describes the distance of a number on the number line from 0 without considering which direction from zero the number lies. The absolute value of a number is never negative. The absolute value of 2 + 7 is 5.

Has two solutions x = a and x = -a because both numbers are at the distance a from 0. ... An absolute value equation has no solution if the absolute value expression equals a negative number since an absolute value can never be negative.

7 0
3 years ago
Other questions:
  • Please help meeeeeeee ASAP
    14·1 answer
  • create three different drawings showing a number of rectangles and circle on which the ratio of rectangle to circles is 3;1
    14·1 answer
  • Please help me with #6
    15·2 answers
  • Find the equation of a line given the point and slope below. (-3, 1) m= 1/3​
    13·1 answer
  • How are operations with radical expressions similar to operations with variables
    15·1 answer
  • In the blank next to the distribution shape, type YES if is most often appropriate to use the mean, or NO if it is not.
    9·1 answer
  • Given A={1,2,3}, B={2,4,6} and C={1,2,3,4,5,6}, then A ∩ (B ∩ C) =
    11·1 answer
  • . A board game has dice shaped like octahedrons. Each edge of the dice has length 1 cm and the h= √ 2/ 2 cm. What is the volume
    11·1 answer
  • Find the sum or type<br> "impossible”<br> [1 -2 1] + [4 -5 -6] ]<br> [[?]<br> [ ]]
    7·1 answer
  • Math question please help!! Linear equations, quite simple
    6·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!