Question

in 1950 the use of coal in the us was 114.6 million tons. the use of coal has decreased by 6.6% per year since then. estimate the amount of coal used in the US in 2010.

Answer 1

Amount of estimated coal that has been used in the year 2010 = 23.1 million tons

Explanation:

In 1950 the use of coal in the us was 114.6 million tons

The use of coal has decreased by 6.6% per year since then

The time would be 2010 - 1950 = 60 years

Let the estimate amount used in the year 2010

⇒ 114.6 = x(1 + 0.066 × 60)

⇒ 114.6 = x × 4.96

⇒ x = 23.1

Therefore, Amount of estimated coal that has been used in the year 2010 = 23.1 million tons

Answer 2

For this problem, it could be mistaken to be decay rate which is exponential. But this is actually logical to simple interest in economics.The difference would be, the principal amount and future amount are interchanged because it is decreasing. Using the formula for simple interest,

Year 1950 = Year 2010 (1 + rate*time)
The time would be 2010-1950 = 60 years

114.6 = x(1 + 0.066*60)
x = 23.1 million tons