If the demand for aluminium is increasing at the rate of 8 % per annum, approximately how long will it take be

Question

If the demand for aluminium is increasing at the rate of 8 % per annum, approximately how long will it take before total consumption doubles?

The growth in consumption of a commodity may be represented by an exponential relationship of the form:

C=Co ert

Answer 1

c(t)=c(0)e^rt
at t=0, c(t)=c(0)
If c(t) doubles,
2c(0)=c(0)e^0.08t
2=e^0.08t
ln (2) = ln (e^0.08t)
ln (2) = 0.08t
t= ln(2) / 0.08
t=8.66
In about 8.66 years, consumption will double.

Answer 2

Joe L is spot on and gives two answers because "8% a year" could mean either a total growth of 8% between now and next year, or a current rate of 8% a year which actually gives 8.3% more in 12 months because of compounding. Cidyah is assuming immediate compounding and Krazykyn is assuming the other possibility.

Real world warning: we know how much demand grew last year, but have no way of being sure what will happen next year, let alone for the next 9 years.

Answer 3

If it's compounding annually, then

1 X 1.08^x = 2

1.08^x = 2

Take logs

x log 1.08 = log 2

.033423 x = .30103

x = 9 years

By the way. Your problem states that consumption is increasing at a rate of 8% ANNUALLY. If you use the exponential e as the basis for rate of increase, you are implying that the rate of increase is INSTANTANEOUS. Therefore, you will get a faster rate of growth, and a shorter time period (in the order of 8.5 years) to double consumption.

Answer 4

Very simple way to handle this kind of question:
ln(2)/ln(1.08)
________________________________________
KrazyKyngeKorny(Krazy, not stupid)
¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯