# College Algebra

The rodent population in a city is currently estimated at 30,000 and is growing according to the Malthusian model. If it is expected to double every 9 years, when will the population reach one million? (Round your answer to one decimal place.)

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1. No idea what the Malthusian model is, but I will do it my way

P = 30,000 e^(kt) , where k is constant and t is years

given:when t = 9, P = 60,000

30000 e^(9k) = 60000
e^(9k) = 2
9k = ln2
k = ln2/9

P = 30,000 e^((ln2/9)t)
when is P = 1,000,000 ?
30,000 e^((ln2/9)t) = 1,000,000
e^((ln2/9)t) = 100/3
ln2/9 t = ln100 - ln3
t = 9(ln100 - ln3)/ln2 = 45.5 years

alternate way:
since there is doubling effect, we can use base 2 in our exponential term
P = 30,000 (2)^(t/9)
30,000 2^(t/9) = 1,000,000
2^(t/9) = 100/3
log (2^(t/9)) = log(100/3)
t/9 log2 = log100 - log3
t/9 = (2 - log3)/log2
t = 9(2 - log3)/log2 = 45.5 years

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posted by Reiny
2. Thank you so much for your help!

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