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Chapter 1: Problem 25

The economy of Argentina as measured by its Gross Domestic Product (GDP) is shrinking at a rate of \(2.6 \%\) per year. In 2015 , the GDP of Argentina was \(\$ 630\) billion. Which of the following functions represents Argentina's GDP, \(A\), in billions of dollars, \(y\) years since \(2015 ?\) A) \(A(y)=630-(1-0.26) y\) B) \(A(y)=630(1-0.26)^y\) C) \(A(y)=630-(1-0.026) y\) D) \(A(y)=630(1-0.026)^y\)

Short Answer

Expert verified
The function that represents Argentina's GDP in billions of dollars, \(y\) years since 2015, is: \(A(y)=630(1-0.026)^y\)

Step by step solution

01

Identify exponential decay functions

Between the given options, we can identify that both option B and option D represent exponential decay functions because they have the form \(A(y)=630(1-r)^y\), where \(r\) is the decay rate.
02

Convert the decay rate

We have been given a decay rate of \(2.6\%\) per year. To use this percentage in the function, we need to convert it to a decimal. We can do that by dividing by 100: \(2.6\% = 2.6 / 100 = 0.026\)
03

Compare the options

Now that we have the decay rate as a decimal, we can compare our options to see which function accurately represents Argentina's GDP: Option B: \(A(y)=630(1-0.26)^y\) In this option, the decay rate is 0.26, which is not equal to our calculated decay rate of 0.026. Option D: \(A(y)=630(1-0.026)^y\) In this option, the decay rate is 0.026, which is equal to our calculated decay rate.
04

Conclude the answer

Since option D has the exponential decay format and the correct decay rate, we can conclude that the function that represents Argentina's GDP in billions of dollars, \(y\) years since 2015, is: \(A(y)=630(1-0.026)^y\)

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