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# C3 Question??? watch

1. This question is from Paper G solomon for C3 edexcel...

(6.)
The populations in thousands, P, of a town at time t years after 1st january 1980 is modelled by the formula

P = 30 + 50e^0.0022t

Use this model to estimate:

(a) the population of the town on first january 2010,

(b) the year in which the populaton first exceeds 84 000,

The population in thousands, Q, of another town is modelled by the formula

Q = 26 + 50e^0.003t

(c) Show that th evalue of t when P = Q is a solution of the equation

t = 1000 ln (1 + 0.08e^-0.002t)

Anyone know how to do part (c)????
2. 30 + 50e^0.002t=26 + 50e^0.003t

4= 50e^0.003t - 50e^0.002t

the divide everything by 50

4/50 = e^0.003t - e^0.002t

4/50 = e^0.002t(e^0.001t-1)

0.08/e^0.002t = e^0.001t-1

0.08/e^0.002t + 1 = e^0.001t

then take ln of the lhs

ln(0.08/e^0.002t + 1) =0.001t

btw 0.08/e^0.002t = 0.08e^-0.002t
therefore

ln(0.08e^-0.002t+1)= 0.001t
then multiply both sides by 1000

1000ln(0.08e^-0.002t+1)=t
hope it helped

khalid
3. hey thanx a lot...

i was really stuck on that one

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