Exponential growth (easy(?) question):

In summary, the conversation discussed the difference in GDP per capita between Morocco and France and made a prediction about when the two countries' GDP per capita will be equal.
  • #1
beaf123
41
0
Back to how income differences is explained in neoclassical theory, one can ask the question why GDP/capita is $5200 in Morocco and $35 500 in France. Real GDP per capita has grown at a rate of about 3.5% from 2008– 2012, GDP/capita in France grew in the same period at a rate of 1.1%. (http://data.worldbank.org/indicator/NY.GDP.PCAP.KD.ZG/countries/1W-XQ-EG-SY-IR-SA?display=default)
If this holds up GDP/ capita in Morocco will be the same as the one in France in X years.

So I can't find the X:

I have tried:

5200e^ln(1.035)t = 35 500e^ln(1.01)t

But I can't solve it..:-(

Hope someone can help me!:)
 
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  • #2
The GDP per capita in Morocco after ##n## years will be ##5200(1.035)^n##, and in France it will be ##35500(1.011)^n##. Now set these equal to each other and solve for ##n##:
$$5200(1.035)^n = 35500(1.011)^n$$
or equivalently,
$$\left(\frac{1.035}{1.011}\right)^n = \frac{35500}{5200}$$
Taking logs of both sides should get you the answer quickly from here.
 

What is exponential growth?

Exponential growth is a type of growth in which the quantity of a specific variable increases at an increasing rate over time. This means that the growth rate itself is also increasing.

What factors contribute to exponential growth?

Exponential growth is typically driven by factors such as a large initial population, a high reproductive rate, and an abundant food supply. These factors allow for a rapid increase in population size.

How is exponential growth different from linear growth?

Exponential growth differs from linear growth in that the rate of growth for exponential growth is constantly increasing, while linear growth has a constant rate of increase. This results in a much steeper curve for exponential growth compared to a more gradual increase for linear growth.

What are some real-life examples of exponential growth?

Some real-life examples of exponential growth include population growth, the spread of diseases, and the growth of technology. These all demonstrate the compounding effect of exponential growth over time.

What are the potential consequences of exponential growth?

Exponential growth can lead to rapid depletion of resources and overpopulation, which can have negative impacts on the environment and society. It can also result in a rapid increase in demand for goods and services, leading to economic challenges. Proper management and control of exponential growth is important to avoid these potential consequences.

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