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Answer :
Answer:
2071
Step-by-step explanation:
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Answer:
2071
Step-by-step explanation:
Since, the decline model follows exponential- decay model
thus,
[tex]P = P_oe^{kt}[/tex]
Here,
P₀ is the initial consumption
t is the time in years
P is the consumption after t years
k is the decay constant
now,
1985 is the base year, thus for year 1985; t = 0
at t = 0, P = 80
Therefore,
[tex]80 = P_oe^{k(0)}[/tex]
or
P₀ = 80 pounds
also,
in the year 1996 i,e t = 1996 - 1985 = 11 years
P = 67 pounds
thus,
[tex]67 = 80e^{k(11)}[/tex]
or
0.8375 = [tex]e^{k(11)}[/tex]
taking the log both sides, we get
-0.177 = 11k
or
k = - 0.01612
Therefore,
For P = 20 pounds per person
we have
[tex]20 = 80e^{(-0.01612)(t)}[/tex]
or
0.25 = [tex]e^{(-0.01612)(t)}[/tex]
taking natural log both the sides, we get
-1.3863 = (- 0.01612 )(t)
or
t = 85.99 ≈ 86 years
Hence,
the year will be 1985 + 86 = 2071
