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If a town with a population of 10000 doubles in size every 43 years, what will the population be 86 years from now

Sagot :

walshl7813

Answer:This is an exponential growth problem.  If the population doubles periodically, it follows a law like this:

P(t) = P(0)ekt

where P(0) is the initial population at time t=0, and k is a constant with units of years-1.

To find k, let t=0.  Then P(t) = P(0) = initial population = 5000.

Since the population doubles every 12 years, we can write

P(t+12) = 2P(t)

P(0)ek(t+12) = 2[P(0)ekt]

Simplifying,

e12k = 2

k = ln(2) / 12 = 0.0577623 years-1

Finally,

P(t) = 5000e0.0577623t, t in years

Then at t=48 years from now,

P(48) = 5000e(0.0577623 * 48) = 80,000

Step-by-step explanation:

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