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Ivan
2 years ago
10

Mario is paid a salary of $500 plus 8% of sales. Calculate his total income if his sales total $10,890 in the

Mathematics
1 answer:
Gre4nikov [31]2 years ago
7 0

Answer:

His total income is of $1,371.2.

Step-by-step explanation:

His salary is of $500, plus 8% of his sales.

In this question:

Sales of $10,890. So his salary is given by:

S = 500 + 0.08*10890 = 500 + 871.2 = 1371.2

His total income is of $1,371.2.

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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)^xwhere 
y is the final amount remaining after t years of decaya is the initial amountb 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 decaya is the initial amountb 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.

3 0
2 years ago
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