precalculus help

Question

Suppose that the world's current oil reserves is r=1910 billion barrels. If, on average, the total reserves is decreasing by 25 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.) 9 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 again Mark,

Here we have a classic example of a linear model. So, what do we know... we're starting with 1910 billion barrels, and we're decreasing by 25 billion barrels each year.

(a)

Our starting point is also known as the y-intercept, and the rate of 25 billion barrels per year is our slope. (note that the slope is negative since we're decreasing by 25B barrels.)

Putting this into our y=mx+b setup, we get:

r = 1910 - 25t

(b)

Using our model, when plugging in t = 9 we get:

r = 1685

(c)

we want to know how many years till there's nothing left... in other words, when will r = 0?

plug in r = 0 and solve for t:

0 = 1910 - 25t

t = 76.4 years

Hope this helps