What is the Annual Percentage Growth in Energy Consumption from 1996 to 2025?

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Homework Help Overview

The discussion revolves around calculating the annual percentage growth in energy consumption from 1996 to 2025, with specific figures provided for energy usage in terajoules and projected power needs. Participants are also exploring a related problem regarding population growth and its implications.

Discussion Character

  • Mixed

Approaches and Questions Raised

  • Participants are attempting to calculate percentage growth using energy consumption data and projections for future power needs. There are questions about the accuracy of calculations and the interpretation of results. Some participants are also exploring logarithmic methods to solve a population growth problem.

Discussion Status

There is ongoing dialogue about the calculations presented, with some participants questioning the clarity of certain statements and offering alternative approaches. While some figures have been confirmed, there is no explicit consensus on the interpretations of the results or the methods used.

Contextual Notes

Participants are working within the constraints of homework guidelines, which may limit the types of assistance they can provide to one another. The discussion includes varying assumptions about energy projections and population growth rates.

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Homework Statement



In 1996 the total energy used in the world was 400 million terajoules = 400 exajoules (EJ)= 4 x 10^20J . Projections for energy use vary, but generally it is expected that between 20 and 30TW will be needed by 2025.

(a) What percentage growth in energy consumption on an annual basis does
the increase between 1996 and 2025 represent?

Homework Equations



Energy = Power x Time

The Attempt at a Solution



Taking an average of 25TW of power used in 2025:
25TW * (356*24*3600) = 7.88 x10^20 J

To find percentage: (percentage)^29 * 4 x 10^20J = 7.884 x10^20 J

Re-arranging to find totally percentage increase of 102.3% each year. So an annual increase of ~2.3% over the 29 years.

Is this correct? Thank you!
 
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Also this one please?

1. Homework Statement
Assume the Earth's human population increases at 1.25% a year from its present 6.5 billion and reaches 15 billion people (instead of the maximum 12 billion projected by the UN). How many years will that take?


The Attempt at a Solution



8.5 billion = 6.5 billion * (1.0125)^ (years)

1.307 = (1.0125) ^ years

Through trial and error I found years = 21 to 22 years.

How can I re-arrange it to find a more accurate answer please? Thanks!
 
Jenkz said:

Homework Statement



In 1996 the total energy used in the world was 400 million terajoules = 400 exajoules (EJ)= 4 x 10^20J . Projections for energy use vary, but generally it is expected that between 20 and 30TW will be needed by 2025.

(a) What percentage growth in energy consumption on an annual basis does
the increase between 1996 and 2025 represent?

Homework Equations



Energy = Power x Time

The Attempt at a Solution



Taking an average of 25TW of power used in 2025:
25TW * (356*24*3600) = 7.88 x10^20 J

To find percentage: (percentage)^29 * 4 x 10^20J = 7.884 x10^20 J

Re-arranging to find totally percentage increase of 102.3% each year. So an annual increase of ~2.3% over the 29 years.

Is this correct? Thank you!
2.37% per annum is correct, but the in bold doesn't make sense. 2.37% per year is the total percent increase each year... not 102.37%.
 
Jenkz said:
Also this one please?

1. Homework Statement
Assume the Earth's human population increases at 1.25% a year from its present 6.5 billion and reaches 15 billion people (instead of the maximum 12 billion projected by the UN). How many years will that take?

The Attempt at a Solution



8.5 billion = 6.5 billion * (1.0125)^ (years)

1.307 = (1.0125) ^ years

Through trial and error I found years = 21 to 22 years.

How can I re-arrange it to find a more accurate answer please? Thanks!

n = log_{1.0125} \left( \frac{8.5}{6.5} \right) = 21.595
 
Oh yeah.. that doesn't really make sense :/

Thank you for your help : D!