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

[Jenkz]

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!

 

[Jenkz]

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!

 

[tedbradly]

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%.

 

[tedbradly]

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!

$$n = log_{1.0125} \left( \frac{8.5}{6.5} \right) = 21.595$$

 

[Jenkz]

Oh yeah.. that doesn't really make sense :/

Thank you for your help : D!