MATH SOLVE

2 months ago

Q:
# I need help asap( whoever answers will have Brainlest)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)?

Accepted Solution

A:

a. The Greek crisis began when the government borrowed more money that they can repay, so the Greek crisis is a debt crisis. The Greek debt crisis originated from the Greek’s government wasteful and excessive expenditure; especially in public workers’ salaries and overgenerous pension plans. As a result, Greek’s economy became week, corrupt, and incompetent, so the Government had to resort to a massive debt just to function. Debt-to-GDP ratio skyrocketed, which translating in the collapse an subsequent crisis of Greek’s economy.

b. To solve this, we are going to use the standard decay function [tex]y=a(1-b)^x[/tex]where

[tex]y[/tex] is the final amount remaining after [tex]t[/tex] years of decay[tex]a[/tex] is the initial amount[tex]b[/tex] is the decay rate in decimal form

[tex](1-b)[/tex] is the decay factor

[tex]x[/tex] is the time in years

I will tell Greece to cut their expending by 25%

To find our decay factor [tex](1-b)[/tex], we are going to convert the rate from percentage to decimal; to do it, we are going to divide the rate by 100%

[tex]b= \frac{25}{100} [/tex]

[tex]b=0.25[/tex]

Decay factor = [tex](1-b)[/tex]

Decay factor = [tex](1-0.25)[/tex]

Decay factor = (0.75)

We can conclude that our decay factor is (0.75)

c. To solve this, we are going to use the standard decay function [tex]y=a(1-b)^x[/tex] from our previous point.

where

[tex]y[/tex] is the final amount remaining after [tex]t[/tex] years of decay[tex]a[/tex] is the initial amount[tex]b[/tex] is the decay rate in decimal form

[tex](1-b)[/tex] is the decay factor

[tex]x[/tex] is the time in years

We know from our problem that the initial debt in 2009 was $500 billion, so [tex]a=500,000,000,000[/tex]; we also know fromm our previous calculation that our decay factor is (0.75), so lets replace those values in our function:

[tex]y=a(1-b)^x[/tex]

[tex]y=500,000,000,000(0.75)^x[/tex]

We can conclude that the function that model this debt situation is: [tex]y=500,000,000,000(0.75)^x[/tex].

d. Greece will be debt-free when heir debt is zero. Translating this into our model, Greece will be debt-free when [tex]y=0[/tex]. Since we will need logarithms to find the time [tex]x[/tex], and the logarithm of zero is not defined, we are going to use a small value for [tex]y[/tex], so we can use logarithms to find [tex]x[/tex].

Let [tex]y=1[/tex]. After all, a $1 debt for a country is practically the same as being debt-free.

[tex]y=500,000,000,000(0.75)^x[/tex]

[tex]1=500,000,000,000(0.75)^x[/tex]

Now, we can solve for [tex]x[/tex] using logarithms:

[tex] \frac{1}{500,000,000,000} =(0.75)^x[/tex]

[tex](0.75)^x= \frac{1}{500,000,000,000} [/tex]

[tex]ln(0.75)^x=ln(\frac{1}{500,000,000,000})[/tex]

[tex]xln(0.75)=ln(\frac{1}{500,000,000,000})[/tex]

[tex]x= \frac{ln(\frac{0.01}{500,000,000,000})}{ln(0.75)} [/tex]

[tex]x=93.6[/tex]

We can conclude that, with me in charge, Greece will be debt free after 93.6 years. I won't reconsider my answer b. Even tough 93.6 years is a lot of time, cutting the public expense more than 25% will have worse consequences for the economy of the country than the debt itself.

b. To solve this, we are going to use the standard decay function [tex]y=a(1-b)^x[/tex]where

[tex]y[/tex] is the final amount remaining after [tex]t[/tex] years of decay[tex]a[/tex] is the initial amount[tex]b[/tex] is the decay rate in decimal form

[tex](1-b)[/tex] is the decay factor

[tex]x[/tex] is the time in years

I will tell Greece to cut their expending by 25%

To find our decay factor [tex](1-b)[/tex], we are going to convert the rate from percentage to decimal; to do it, we are going to divide the rate by 100%

[tex]b= \frac{25}{100} [/tex]

[tex]b=0.25[/tex]

Decay factor = [tex](1-b)[/tex]

Decay factor = [tex](1-0.25)[/tex]

Decay factor = (0.75)

We can conclude that our decay factor is (0.75)

c. To solve this, we are going to use the standard decay function [tex]y=a(1-b)^x[/tex] from our previous point.

where

[tex]y[/tex] is the final amount remaining after [tex]t[/tex] years of decay[tex]a[/tex] is the initial amount[tex]b[/tex] is the decay rate in decimal form

[tex](1-b)[/tex] is the decay factor

[tex]x[/tex] is the time in years

We know from our problem that the initial debt in 2009 was $500 billion, so [tex]a=500,000,000,000[/tex]; we also know fromm our previous calculation that our decay factor is (0.75), so lets replace those values in our function:

[tex]y=a(1-b)^x[/tex]

[tex]y=500,000,000,000(0.75)^x[/tex]

We can conclude that the function that model this debt situation is: [tex]y=500,000,000,000(0.75)^x[/tex].

d. Greece will be debt-free when heir debt is zero. Translating this into our model, Greece will be debt-free when [tex]y=0[/tex]. Since we will need logarithms to find the time [tex]x[/tex], and the logarithm of zero is not defined, we are going to use a small value for [tex]y[/tex], so we can use logarithms to find [tex]x[/tex].

Let [tex]y=1[/tex]. After all, a $1 debt for a country is practically the same as being debt-free.

[tex]y=500,000,000,000(0.75)^x[/tex]

[tex]1=500,000,000,000(0.75)^x[/tex]

Now, we can solve for [tex]x[/tex] using logarithms:

[tex] \frac{1}{500,000,000,000} =(0.75)^x[/tex]

[tex](0.75)^x= \frac{1}{500,000,000,000} [/tex]

[tex]ln(0.75)^x=ln(\frac{1}{500,000,000,000})[/tex]

[tex]xln(0.75)=ln(\frac{1}{500,000,000,000})[/tex]

[tex]x= \frac{ln(\frac{0.01}{500,000,000,000})}{ln(0.75)} [/tex]

[tex]x=93.6[/tex]

We can conclude that, with me in charge, Greece will be debt free after 93.6 years. I won't reconsider my answer b. Even tough 93.6 years is a lot of time, cutting the public expense more than 25% will have worse consequences for the economy of the country than the debt itself.