Answer:
A.) R = 2160 -15t
B.) 1965 billion barrels
C.) 144.00 years
Explanation:
Given current oil reserves of 2160 billion barrels, decreasing by 15 billion barrels per year, you want an equation for reserves R as a function of years t from now, R(13), and the value of t when R = 0.
A) Reserves
Each year reserves decrease by 15 billion barrels. That means after t years, they will have decreased by 15t billion barrels.
Since are starting with 2160 billion barrels, the amount remaining is that amount with the amount of decrease being subtracted from it:
R = 2160 -15t
B) In 13 years
The value in 13 years is found by putting 13 where t is in the equation, and doing the arithmetic.
R = 2160 -15·13 = 1965
In 13 years, reserves ill be 1965 billion barrels.
C) Depletion
To find when reserves are zero, we solve the equation for that:
0 = R
0 = 2160 -15t . . . . . use the expression for R
15t = 2160 . . . . . . add 15t
t = 2160/15 = 144 . . . . divide by 15
Reserves will be depleted in 144 years.