One model for the time it will take for the world's oil supply to be depleted is given by the equation T = 14.29 ln(0.00411r + 1), where r is the estimated world oil reserves in billions of barrels and T is the time, in years, before that amount of oil is depleted. Use this equation to determine how many barrels of oil are necessary to last 21 years. Round to the nearest tenth.r = _____________ billion barrels

Question
Asked Oct 29, 2019

One model for the time it will take for the world's oil supply to be depleted is given by the equation T = 14.29 ln(0.00411r + 1), where r is the estimated world oil reserves in billions of barrels and T is the time, in years, before that amount of oil is depleted. Use this equation to determine how many barrels of oil are necessary to last 21 years. Round to the nearest tenth.
r = _____________ billion barrels

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Step 1

The time taken for the world’s oil supply to be depleted is given by the equation,

T 14.29ln(0.00411r 1
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T 14.29ln(0.00411r 1

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Step 2

Given T = 21 years

Substitute the value of T...

T 14.29 1n(0.00411r +1)
21 14.29ln(0.0041 1r 1)
21
n(0.00411r1 =
14.29
21
0.0041 1r 1 e
14.29
21
0.00411r e.25,
1
21
14.29
-1
r =
0.00411
r 814.43
r 814 billion barrels
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T 14.29 1n(0.00411r +1) 21 14.29ln(0.0041 1r 1) 21 n(0.00411r1 = 14.29 21 0.0041 1r 1 e 14.29 21 0.00411r e.25, 1 21 14.29 -1 r = 0.00411 r 814.43 r 814 billion barrels

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