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
Add 1/2 liter,3/4 liter and 7/8 liter
LUCKY_DIMON [66]
First, find a lowest common denominator. The lcd in this equation os 8 so your new fractions would be 4/8, 6/8, and 7/8. You add the numerators (top numbers), which equals 17/8. Then you simplify to 2 1/8 liters.
5 0
3 years ago
Please help me out!!! :) 
Olin [163]

it would be > because the square root of 2 is more than 1.

8 0
3 years ago
Read 2 more answers
A water sprinkler sends water out in a circular pattern. How large is the watered area if the radius of the watering pattern is2
Mamont248 [21]

Answer:

Step-by-step explanation:

Simply put, it is similar to finding the area of a circle.

Therefore, a=pi*r^2

a=pi*23^2

a=529pi

a=1661.9 ft^2

6 0
2 years ago
What is the equation of a line that has a y-intercept of 4 and an x-intercept of -2?​
Furkat [3]

Answer:

y = 2x + 4

Step-by-step explanation:

Two points on this line are (-2, 0) and (0, 4).  Going from the first to the second, x increases by 2 (this is the 'run') and y increases by 4 ('rise').

Thus, the slope of this line is m = rise / run =  4/2 = 2

Using the slope-intercept formula, we get y = mx + b = 2x + b

Let x = -2 and y = 0 to find b:  0 = 2(-2) + b, so b = 4, and the desired equation is then:

y = 2x + 4

6 0
3 years ago
Find the values of z and y pls :)
stellarik [79]
Measure of z is 116°.The measure of y is 48°.Hope this helps.
4 0
2 years ago
Other questions:
  • How do you reflect over y axis
    5·2 answers
  • 290°, rotate the terminal side 20° more in the counterclockwise direction
    8·1 answer
  • What is the value of r?<br> Round your final answer to the nearest whole number.
    13·2 answers
  • Please help asap 30 pts
    9·1 answer
  • Jada sells ground paprika.
    10·2 answers
  • What is the answer to ... -5 - 3w = 7
    9·1 answer
  • For a certain recipe, Ben takes a 5 1/2 -cup sack of sugar and uses all but 1 3/4 cups.
    8·1 answer
  • I will give barinest if solved
    14·1 answer
  • A family makes rods by cutting plastic pipes that are 5 feet long into 8 rods, how long are each rod?
    12·1 answer
  • Help plz !! I will give you points or anything !!
    14·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!