# Finding the rate with T=1/r ln (rR/C + 1) ?

1. Jan 14, 2009

### rought

I am completely at a loss with this question

If one assumes that the current growth rate of consumption remains constant, the then expiration time in years is give by: T=1/r ln (rR/C + 1) where C = current consumption, r = current growth rate of consumption, and R = resource size. Suppose that the world's consumption of oil is growing at the rate of 7% per year (r = 0.07) and the current consumption is approximately 17 X 10^9 barrels per year. Fins the expiration time for the following estimates of R

a. R ≈ 1691 X 10^9 barrels (estimate of remaining crude oil)

b. R ≈ 1881 X 10^9 barrels (estimate of remaining crude plus shale oil)

2. Jan 15, 2009

### Unco

You're being asked to find T, given an equation and values for r, R and C to substitute in. Assuming the units agree (they are not specified in the definitions of C, r and R), this is just a straight calculation!

3. Jan 15, 2009

### rought

Alright I followed along and did a straight calculation heres what I got:

a. T=1/.07 x ln(.07(1691 x 10^9)/17 x 10^9)

T=1/.07 x ln(6.9876) which = T ≈ 27.7735

b.a. T=1/.07 x ln(.07(1881 x 10^9)/17 x 10^9)

T=1/.07 x ln(7.7453) which = T ≈ 29.2441

Does this seem right?