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Suppose that the world's current oil reserves is R= 2080 billion barrels. If, on average, the total reserves is decreasingby 23 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.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 world's oil reserves will be completely depleted (all used up) approximately_____ years from now.(Round your answer to two decimal places.)

Respuesta :

A)

Since each year the reserves decrease by 23 billion barrels of oil, then after t years, the reserves will decrease by 23t billion barrels of oil.

Substract 23t from 2080 to find an equation that describes the reserves of oil as a function of time:

[tex]R=2080-23t[/tex]

B)

Replace t=13 to find the total oil reserves 13 years from now:

[tex]\begin{gathered} R=2080-23(13) \\ =2080-299 \\ =1781 \end{gathered}[/tex]

Then, 13 years from now, the total oil reserves will be 1781 billions of barrels.

C)

If no other oil is deposited into the reserves (and if the demand of oil does not increase), we can find how many years from now are left until the reserves will be completely depleted by setting R=0 and solving for t:

[tex]\begin{gathered} R=0 \\ \Rightarrow0=2080-23t \\ \Rightarrow23t=2080 \\ \Rightarrow t=\frac{2080}{23} \\ \therefore t=90.43478261\ldots \end{gathered}[/tex]

Then, to two decimal places, the reserves will be completely depleted approximately 90.43 years from now.

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