Plot the following scenarios for per capita GDP on a ratio scale. Assume that per capita GDP in the year 2015 is equal to $10,000. You should not need a calculator or computer program. Use the Rule of 70 to label the value of per capita GDP on the graph in the year listed below.

a. Per capita GDP grows at a constant rate of 5% per year between 2015 and 2085.
b. Per capita GDP grows at 2% per year between 2015 and 2085, speeds up to 7% per year for the next 20 years, and then slows down to 5% per year for the next 28 years.
c. Per capita GDP grows at 7% per year for 50 years and then slows down to 1% per year for the next 140 years.

Answer is explained in the explanation section.

Explanation:

As given, we have to use the 70's rule, which states that, size of the variable will be doubled every 70/x years, if the the yearly growth rate of that variable is x%.

And we are given that,

The Per Capita GDP for year 2015 = $10,000

a) Graphs of the Per Capita GDP are attached in the attachment 1.

So, by using the rule of 70. we have

x = 5% growth rate.

between the years 2015 and 2085.

So, the size of the variable will be doubled every 70/x years, if the yearly growth rate is 5%.

So,

Years = 70/x

Years = 70/5

Years = 14.

It means, per capita GDP will be doubled every 14 years time period.

b) Graphs of the Per Capita GDP are attached in the attachment 2.  

Growth rate = 2%

Between the years 2015 and 2085. then

Growth rate = 7%

For = After 2085 years for 20 years, then

Growth rate = 5%

For = next 28 years.

So,

Years = 70/x

Years = 70/2

Years = 35 years.

It means, per capita GDP will be doubled every 35 years time period.

Now, it speeds up to 7% per year for the next 20 years.

Year = 70/x

Years = 70/7

Years = 10 years

It means, it speeds up to 7% per year for the next 20 years.  per capita GDP will be doubled every 10 years time period.  

Now, if it slows down to 5% per year for the next 85 years then,

years = 70//x

years = 70/5

years = 14 years

 It means, if it slows down to 5% per year for the next 85 years then,  per capita GDP will be doubled every 14 years time period.  

c) Graphs of the Per Capita GDP are attached in the attachment 3.  

Growth rate = 7% per year

For = 50 years and then

Grow rate = 1%

For = next 140 years.

Years = 70/x

Years = 70/7

Years = 10 years

It means, Per capita GDP will be doubled after every 10 years for 50 years.

Now, if it slows down to 1% per year for the next 140 years then,

Years = 70/x

Years = 70/1

Years = 70 years

It means, for next 140 years per capita GDP will be double after every 70 years.

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