Problem Solving Using Linear Equations

Question

Suppose that the world's current oil reserves is  billion barrels. If, on average, the total reserves is decreasing by  billion barrels of oil each year, answer the following:

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

B.)  years from now, the total oil reserves will be  billions 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.)

Answer 1

Hi, Adin!

For this problem, the key is to recognize that we can express the information given in this problem as an equation in slope-intercept form (y=mx+b), where we replace y with R and x with t.

We are given that, right now (at t=0), R = 1,930. Putting this in slope-intercept form, we see that

R = 1,930 = m(0) + b --> 1,930 = 0 + b --> b = 1,930

Next, we are given that R is decreasing by 21 billion barrels per year and the number of years that has passed is given by t. Therefore, out slope must be m = -21. It's important that this value is negative, because the number of barrels must decrease as time passes.

a) Thus, we can write out the equation: R = -21t + 1,930

b) We are given that 7 years has passed, and that we need to solve for the number of barrels (in billions). Therefore, we are solving for R when t = 7.

R = -21(7) + 1,930 --> R = -147 + 1,930 --> R = 1,783

Thus, 7 years from now, the total oil reserves will be 1,783 billion barrels.

c) For this last part, we are being asked to calculate how many years it would take for the oil reserves to be completely used up. In terms of our equation, this means we are solving for t when R = 0.

R = 0 = -21t + 1,930, We can move the -21t to the left side by adding 21t to both sides.

21t = 1,930, Then we divide both sides by 21 to solve for t

t = 91.9047619 We can then round this answer to two decimal places

t = 91.90

Thus, if no other oil is deposited into the reserves, the world's oil reserves will be completely depleted in approximately 91.90 years.

I hope that this explanation was helpful!