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

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SUMMARY

The discussion focuses on calculating the expiration time of oil resources using the formula T=1/r ln(rR/C + 1), where C is the current consumption, r is the growth rate of consumption, and R is the resource size. With a growth rate (r) of 7% per year and current consumption (C) of approximately 17 billion barrels per year, the expiration times for two estimates of remaining resources (R) were calculated. For R ≈ 1691 billion barrels, the expiration time (T) is approximately 27.77 years, and for R ≈ 1881 billion barrels, T is approximately 29.24 years. These calculations confirm the method's accuracy when substituting the given values into the formula.

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rought
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I am completely at a loss with this question :confused:

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)
 
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rought said:
I am completely at a loss with this question :confused:

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. Fin[d] the [approximate] expiration time[/color] 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)
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!
 
Unco said:
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!

Alright I followed along and did a straight calculation here's 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?
 

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