Question

suppose that the worlds current oil reserves is r = 1960 billion barrels. if, on average, the total reserves is decreasing by 21 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.) 11 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.) question help: video message instructor

Explanation:

Step1: Identify 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. In the context of the oil - reserves problem, the initial amount of oil reserves is the y - intercept ($b = 1960$) and the rate of decrease is the slope ($m=-21$). So the linear equation for the remaining oil reserves $R$ in terms of $t$ (number of years) is $R=-21t + 1960$.

Step2: Calculate reserves after 11 years

Substitute $t = 11$ into the equation $R=-21t + 1960$. Then $R=-21\times11 + 1960=-231+1960 = 1729$.

Step3: Find the time to depletion

Set $R = 0$ in the equation $R=-21t + 1960$. Then $0=-21t+1960$. Solving for $t$, we get $21t = 1960$, so $t=\frac{1960}{21}\approx93.33$.

Answer:

A. $R=-21t + 1960$
B. $1729$
C. $93.33$