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On a small island there were 32768 deer and only 128 wolves. Statistics gathered revealed that
the wolf population doubled every 3 years and the deer population halved every 6 years.
How many years did it take for the wolf population to overtake the deer population?
Create an algebraic solution to the problem.
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From the condition, we have
D(t) = 32768*1/2)^(t/6) (1)
for deer population and
W(t) = 128*2^(t/3) (2)
for wolves population.
To answer the question, we should solve this equation
D(t) = W(t), or 32768*(1/2)^(t/6) = 128*2^(t/3). (3)
It implies
= 2^(t/3) * 2^(t/6),
or
256 = 2^(t/3 + t/6)
2^8 = 2^(2t/6 + t/6)
2^8 = 2^(3t/6) = 2^(t/2).
Hence, = 8 and t = 2*8 = 16 years. ANSWER
Solved.