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c3 sequences and series question....

this question is from edexcel c3 june 05...

7.
A particular species of orchid is being studied. The population p at time t years after the study
started is assumed to be

p = (2800ae^0.2t) / (1 + ae^0.2t)

, where a is a constant.

Given that there were 300 orchids when the study started,

(a) show that a = 0.12,

(b) use the equation with a = 0.12 to predict the number of years before the population of orchids reaches 1850.

any 1 know how to do part (b)??

thanx in advance
Reply 1
p = (2800ae^0.2t) / (1 + ae^0.2t)
a=0.12, p = 1850

1850 = (2800(0.12)e^0.2t) / (1 + 0.12e^0.2t)
(1 + 0.12e^0.2t)1850 = (2800(0.12)e^0.2t)
1850 + 1850*0.12e^0.2t = 2800(0.12)e^0.2t
1850 = 2800(0.12)e^0.2t - 1850*0.12e^0.2t
1850 = e^0.2t [336 - 222]
0.2t = ln(1850/114)
t = 5ln(925/57) = 13.9 years.