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

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The discussion focuses on calculating the annual percentage growth in global energy consumption from 1996 to 2025, starting with 400 million terajoules in 1996 and projecting an average need of 25TW by 2025. The calculation shows a total percentage increase of approximately 102.3% over 29 years, translating to an annual growth rate of about 2.37%. There is some confusion regarding the interpretation of the percentage increase, clarifying that 2.37% is the correct annual growth rate, not 102.37%. Additionally, a separate query addresses the time required for the human population to grow from 6.5 billion to 15 billion at a rate of 1.25% per year, with calculations suggesting it would take around 21 to 22 years. The discussion emphasizes the need for accurate mathematical rearrangement to improve solution precision.
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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 totaly 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 totaly 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!
 

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