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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

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A line has no thickness, but it does have direction and infinite length.

A line has length but no width, making it a one-dimensional figure. A line is made up of a collection of points that can be stretched indefinitely in opposing directions.

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You look at real estate ads for houses in Naples, Florida. There are many houses ranging from $200,000 to $500,00 in price. The
cricket20 [7]

Answer:

c) skewed to the right.

Step-by-step explanation:

We need to remember that is a distribution is skewed to the right then we have the following condition satisfied:

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And if is skewed to the left then we have:

Mean

If the distribution is symmetric we need to satisfy:

Mean = Median=Mode

For this case since we have most of the values between 200000 and 500000 when we put atypical values like 15000000 that would affect the sample mean and on this case the sample mean would larger than the sample median because the median is a robust measure of central tendency not affected by outliers.

So for this special case we can say that the Mean>Median. And probably the median would be higher than the mode so then we can conclude that the best answer for this case would be:

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Use the following information for the question. Male players at the high school, college and professional ranks use a regulation
Virty [35]

Answer:

13.567%

Step-by-step explanation:

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σ is the population standard deviation = 1.0 ounce

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z = 23.1 - 22.0/1.0

= 1.1

Probability value from Z-Table:

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P(x>23.1) = 1 - 0.86433

P(x>23.1) = 0.13567

Converting to percentage

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Therefore, the percentage of regulation basketballs that weigh more than 23.1 ounces is 13.567%

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