Question

Write a function modeling this debt situation if the initial debt in 2009 was

Answer 1

Answer:

To solve this, we are going to use the standard decay function where

is the final amount remaining after  years of decay is the initial amount is the decay rate in decimal form

is the decay factor

is the time in years

I will tell Greece to decrease their expending by 25%

To find our decay factor , we are going to convert the rate from percentage to decimal; to do it, we are going to divide the rate by 100%

Decay factor =

Decay factor =

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  from our previous point.

where

is the final amount remaining after  years of decay is the initial amount is the decay rate in decimal form

is the decay factor

is the time in years

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

We can conclude that the function that model this debt situation is: .

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

Let . After all, a $1 debt for a country is practically the same as being debt-free.

Now, we can solve for  using logarithms:

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, decreasing the public expense more than 25% will have worse consequences for the economy of the country than the debt itself.