Question

suppose that the worlds current oil reserves is $r = 1840$ billion barrels. if, on average, the total reserves is decreasing by 19 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.) 13 years from now, the total oil reserves will be
$
$ billions of barrels.
c.) if no other oil is deposited into the reserves, the worlds oil reserves will be completely depleted (all used up) approximately
$
$ years from now.
(round your answer to two decimal places.)

Explanation:

Step1: Find the linear - equation form

The general form of a linear equation is $y = mx + b$, where $m$ is the slope and $b$ is the y - intercept. Here, the initial amount of oil reserves $b = 1840$ billion barrels and the rate of decrease $m=- 19$ billion barrels per year. So the linear equation for the remaining oil reserves $R$ in terms of $t$ (years) is $R = 1840-19t$.

Step2: Calculate reserves after 13 years

Substitute $t = 13$ into the equation $R = 1840-19t$. Then $R=1840-19\times13=1840 - 247=1593$ billion barrels.

Step3: Find the time to depletion

Set $R = 0$ in the equation $R = 1840-19t$. Then $0 = 1840-19t$, which can be rewritten as $19t=1840$. Solving for $t$, we get $t=\frac{1840}{19}\approx96.84$ years.

Answer:

A. $R = 1840 - 19t$
B. $1593$
C. $96.84$