Suppose that the world's current oil reserves is

R=1970 billion barrels. If, on average, the total reserves is decreasing by 24 billion barrels of oil each year, answer the following:

A.) Give a linear equation for the total remaining oil reserves, R, in terms of t, the number of years since now. (Be sure to use the correct variable and Preview before you submit.)

R=

B.) 12 years from now, the total oil reserves will bebillions of barrels.

C.) If no other oil is deposited into the reserves, the world's oil reserves will be completely depleted (all used up) approximately___years from now.

(Round your answer to two decimal places.)

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Answered

Answer :

joaobezerra joaobezerra · Answer 1 · 2022-09-09T10:30:47-04:00

From the given situation, we have that:

A) The linear equation is R(t) = 1970 - 24t.

B) 12 years from now, the total oil reserves will be 1682 billions of barrels.

C) Approximately 82.08 years from now.

A linear function is modeled by:

y = mx + b

In which:

m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.

b is the y-intercept, which is the value of y when x = 0, and can also be interpreted as the initial value of the function.

For this problem, the parameters are given as follows:

b = 1970, m = -24.

Hence the linear function is:

R(t) = 1970 - 24t.

For item b, the amount is of R(12), hence:

R(12) = 1970 - 24(12) = 1682.

12 years from now, the total oil reserves will be 1682 billions of barrels.

For item c, we have to solve for t when R(t) = 0, hence:

1970 - 24t = 0

24t = 1970

t = 1970/24

t = 82.08.

Approximately 82.08 years from now.

More can be learned about linear functions at https://brainly.com/question/24808124

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