Question

I need help asap( whoever answers will have Brainlest)

Answer 1

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 $y=a(1-b)^x$where 
$y$ is the final amount remaining after $t$ years of decay$a$ is the initial amount$b$ is the decay rate in decimal form 
$(1-b)$ is the decay factor 
$x$ is the time in years

I will tell Greece to cut their expending by 25%
To find our decay factor $(1-b)$, we are going to convert the rate from percentage to decimal; to do it, we are going to divide the rate by 100%
$b= \frac{25}{100}$
$b=0.25$
Decay factor = $(1-b)$
Decay factor = $(1-0.25)$
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 $y=a(1-b)^x$ from our previous point. 
where
$y$ is the final amount remaining after $t$ years of decay$a$ is the initial amount$b$ is the decay rate in decimal form 
$(1-b)$ is the decay factor 
$x$ is the time in years

We know from our problem that the initial debt in 2009 was $500 billion, so $a=500,000,000,000$; we also know fromm our previous calculation that our decay factor is (0.75), so lets replace those values in our function:
$y=a(1-b)^x$
$y=500,000,000,000(0.75)^x$

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

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

Let $y=1$. After all, a $1 debt for a country is practically the same as being debt-free.
$y=500,000,000,000(0.75)^x$
$1=500,000,000,000(0.75)^x$

Now, we can solve for $x$ using logarithms:
$\frac{1}{500,000,000,000} =(0.75)^x$
$(0.75)^x= \frac{1}{500,000,000,000}$
$ln(0.75)^x=ln(\frac{1}{500,000,000,000})$
$xln(0.75)=ln(\frac{1}{500,000,000,000})$
$x= \frac{ln(\frac{0.01}{500,000,000,000})}{ln(0.75)}$
$x=93.6$

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.