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Chapter 5: Problem 44

Interpreting the News You hear the following on your local radio station's business news: "The economy last year grew by \(1 \%\). This was the second year in a row in which the economy showed a \(1 \%\) growth." This means that, in dollar terms, the economy grew more last year than the year before. Why?

Short Answer

Expert verified
The economy grew more in dollar terms last year than the year before because the base value for each year's growth calculation was different. The base value for the second year was larger (1.01X) than the base value for the first year (X). This is because the growth in the first year added to the initial size of the economy. Since the second year's base value was larger, a 1% growth of it resulted in a higher growth in dollar terms compared to the first year, despite having the same percentage growth.

Step by step solution

01

Understand the concept of percentages

Percentages are used to express a number or a ratio as a fraction of 100. In this case, when we say that the economy grew by 1% for two consecutive years, it means that both years had growth but the base (or the initial value) for each year is different.
02

Determine the starting point

Let's assume that the size of the economy at the beginning of the first year was \(X\) dollars.
03

Calculate the growth during the first year

During the first year, the economy grew by 1%. So, the growth during the first year, in dollar terms, would be \(1\%\) of \(X\), which is \(0.01X\), and the size of the economy at the end of the first year would be \((1 + 0.01)X = 1.01X\).
04

Calculate the growth during the second year

During the second year, the economy again grew by 1%. The base for the second year is \(1.01X\), which is the size of the economy at the end of the first year. So, the growth during the second year, in dollar terms, would be \(1\%\) of \(1.01X\), which is \(0.01(1.01X)\).
05

Compare the growth in dollar terms for both years

Now let's compare the growth in dollar terms for both years: First year growth: \(0.01X\) Second year growth: \(0.01(1.01X)\) Since \(1.01X\) is greater than \(X\), it means that the second year growth (in dollar terms) will be greater than the first-year growth. Thus, it can be concluded that although the economic growth percentage is the same (1%) for both years, the economy has grown more in dollar terms in the last year than the year before.

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