Can someone please help on this portfolio? I've been stuck on it for several days and i've only got task 1
I chose Cape Coral for the population that increased, and Fort Lauderdale as the one that decreased.
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.
Task 3
Greece is currently experiencing a financial crisis.
a. Research the financial crisis in Greece and summarize it in one-two
paragraphs.
b. You are in charge. By what percentage will you tell Greece to cut their
spending? What is the decay factor?
c. Write a function modeling this debt situation if the initial debt in 2009 was
$500 billion and using the decay factor found in (b). Let y be measured in
billions of dollar and x represent the number of years since 2009.
d. When will Greece be debt-free if you are in charge? Should you reconsider
your answer to (b)?
where do you get stuck?
what data did you collect?
To get you started, suppose that the city grew from
1.2 million to 2.1 million in 15 years. Then to find the rate of growth, you solve
(1+r)^15 = 2.1/1.2 = 1.75
1+r = 1.75^(1/15) = 1.038
r = 0.038 or 3.8% per year
To find when the population was 1.83 million, solve
1.038^n = 1.83/1.2 = 1.525
n log 1.038 = log 1.525
n = (log 1.525)/(log 1.038) = 11.31
so, that would be in the 12th year
note that if r is negative, that means the population is decreasing.
Now see what you can do, and show some results if you need more help.
So, what's the answer? I don't get it I am taking it right now
Task 2:
a. To find a city that has experienced population growth, you can start by conducting some research. Look for cities that have had consistent increases in population over time. Once you have identified a city, determine its population on January 1st of a certain year. This data is typically available through government records, census data, or reliable sources such as statistical agencies. Note the population for that specific year.
Next, you need to write an exponential function to represent the city's population growth over time. The exponential function takes the form y = ab^x, where 'y' represents the population, 'x' represents the number of years that have passed, 'a' represents the initial population at year 0 or the starting point, and 'b' represents the growth rate as a decimal or fraction.
In this case, you will have a specific value for the population of the city on January 1st of a certain year. Let's say the initial population in that year is 'P0'. You will also know the population 'P' after a certain number of years 'x'. With this information, you can calculate the growth rate 'b' using the formula:
b = (P / P0)^(1/x)
Substituting the known values, you will be able to determine the exponential function and describe the variables and numbers used in your equation.
b. To find another city that has experienced a population decline, follow a similar process as part (a). Look for cities that have had consistent decreases in population over time. Determine the population of this city on January 1st of the same year that you chose for part (a). Note the population for that specific year.
Just like in part (a), you will need to write an exponential function to represent the city's population decline over time. The exponential function will still take the form y = ab^x, but this time 'a' will represent the larger initial population at year 0, and 'b' will represent the decay rate as a decimal or fraction.
To find the decay rate, use the formula:
b = (P0 / P)^(1/x)
Again, substitute the known values to determine the exponential function and describe the variables and numbers used in your equation.
c. In this part, you need to explain the similarities and differences between the equations derived in parts (a) and (b). Compare the structures of the exponential functions, the values of 'a' and 'b' in each equation, and how they relate to population growth or decline.
d. To determine the year when the population of city (a) first exceeds that of city (b), you need to find the intersection point of the two exponential functions. Set the equations equal to each other, and solve for 'x'. The resulting value of 'x' will represent the number of years since the observed year for which the population of city (a) surpasses that of city (b).
e. To find the year when the population of city (a) is at least twice the size of city (b), set the equation for city (a) equal to 2 times the equation for city (b). Solve for 'x', which represents the number of years since the observed year. The resulting value of 'x' will give you the answer, and you can determine the corresponding year based on the initial year you chose.
Remember to show all your work and explain the steps you take when solving parts (d) and (e).
Task 3:
a. To summarize the financial crisis in Greece in one to two paragraphs, you will need to conduct research on the topic. Look for reliable sources such as news articles, economic reports, or government publications to gather information on the causes, impacts, and current status of the financial crisis. Summarize the key points, including details such as the reasons behind the crisis, the severity of the economic situation, any measures taken to address the crisis, and the overall impact on Greece's economy and society.
b. As the person in charge, you need to determine the percentage by which Greece should cut their spending to address the financial crisis. This decision will depend on various factors such as the country's debt-to-GDP ratio, its ability to generate revenue, and the extent of financial restructuring needed. Consider consulting economic experts, analyzing current economic indicators, or studying successful austerity measures implemented by other countries facing similar challenges.
When you decide on the percentage cut, calculate the decay factor, which represents the decrease in spending over time. The decay factor is equal to (100% - percentage cut) / 100%. For example, if the recommended percentage cut is 10%, the decay factor would be (100% - 10%) / 100% = 90% / 100% = 0.9.
c. Write a function using the decay factor found in part (b) to model Greece's debt situation. The initial debt in 2009 is given as $500 billion. The function will have the general form y = a * (decay factor)^x, where 'y' represents the debt measured in billions of dollars, 'a' represents the initial debt in 2009 ($500 billion), 'x' represents the number of years since 2009, and the decay factor is the value determined in part (b).
Substitute the values into the equation and explain the variables and numbers used in your equation.
d. To determine when Greece will be debt-free based on your chosen decay factor, set the debt function equal to zero and solve for 'x'. This will give you the number of years from 2009 until the debt is projected to be eliminated. Explain your steps and the reasoning behind them when calculating the result. Finally, consider whether you should reconsider your answer to part (b) based on the outcome.