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. round to the nearest tenth of a million tons

Answer 1

Answer:
`0.2\text{ million tons}`

Explanation:

Given: 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 use decreased in x years is given by the formula:-

`y=A(1-r)^x`,

Where A is the initial amount = 14.6 million tons.

r is the rate of decrease in decimal= 0.066

Then, the use of coal in 2010 (after 60 years)=
`y=14.6(1-0.066)^60`

`=14.6(0.934)^(60)\\=14.6*0.016626949\\=0.2427534\approx0.2\text{ million tons}`

Answer 2

The amount of coal used in US in 2010 is
`1.9million\thinspace tons`

Explanation:

Given 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. we have to estimate the amount of coal used in US in 2010.

Let us take the reference 1950 to 0

Amount of coal used in 1950 i.e 0 year is given by the equation

`A=114.6(1-6.6\%)^t`

Now, to calculate the use of coal in 2010 i.e difference of years 2010-1950=60 i.e we have to estimate the amount of coal after 60 yrs is

`A=114.6(1-6.6\%)^(60)`

⇒
`A=114.6(0.934)^(60)`

⇒
`A=1.90544839548\sim1.9million\thinspace tons`

The amount of coal used in US in 2010 is
`1.9million\thinspace tons`