A population P is initially 1000. How do you find an exponential model (growth or decay) for the population after t years if the population P is increases by 200% every 6 years?

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Answer 1 · 2016-07-05T18:50:31

$P = 1000 (3^(1/6))^t$

its +ve growth so the basic equation is

$P = P_o e^{kt}$ {where P = P(t)}

manipulating....
$(P) /P_o = e^{kt}$

$ln (P /P_o) = kt$

$k = 1/t *ln (P /P_o)$

"the population P is increases by 200% every 6 years"

$k = 1/6 *ln ((P_o(1+2)) /P_o)$

$= 1/6 *ln 3 = ln 3 ^ (1/6)$

so

$P = = 1000 (e^(kt)) = 1000 (e^k)^t= 1000 (e^( ln 3 ^ (1/6)))^t$

$= 1000 (3^(1/6))^t$

test

t = 0, P = 1000
t = 6, P $= 1000 (3^(1/6))^6 = 3000$