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The populations P (in thousands) of a certain town in North Carolina, from 2006 through 2012 can be modeled by
P = 5.5ekt,
where t is the year, with
t = 6
corresponding to 2006. In 2008, the population was 7000.

Find the value of k, rounding to 4 decimal places

Then Use the model to predict the population in 2018 (nearest person)

Respuesta :

abidemiokin

Answer:

Step-by-step explanation:

Given the populations P (in thousands) of a certain town in North Carolina, from 2006 through 2012 modeled by

P = 5.5e^kt,

If in 2008, the population was 7000. then;

at t = 2, P = 7000

7 = 5.5e^2k

7/5,5 = e^2k

1.2727= e^2k

Apply ln to both sides

ln 1.272 = lne^2k

ln 1.272= 2k

0.2411 = 2k

k = 0.2411/2

k = 0.1206 (to 4dp)

By 2018, the time t = 12 (2006-2018)

Substitute

P = 5.5e^(0.1206)(12)

P = 5.5e^(1.4468)

P = 5.5(4.2495)

P = 23.3722

P = 23372

Hence the population after 12 years is approx 23,372 populations

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