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Population growth of animal species (math word problem, already partially solved)?
The population growth of an animal species is described by F(t)=400 log (2t + 4) where t is measured in months. a) find population of species after 6 months. b) how many month until population doubles?
I've done a and gotten these results
a) F(6)=400 log (2(6) +4) = 482 months
As for b, this is my interpretation of how I should solve, but I'm not sure.
b) 482*2= 964
964 = 400 log (2t +4)
964/400 = log (2t +4)
2.41 = log (2t +4)
I'm not sure if I'm doing it correctly or if I am correct, where I should go from there.
1 Answer
- ?Lv 57 years ago
Your answer for part a) should be 482 individuals (NOT months)
As for b) your math is good, just continue on with:
10^2.41 = 2t + 4
257 = 2t +4
253 = 2t
126.5 months = t
but this answer is for number of months AFTER the initial 6 months of population growth. I think that the question is asking how long it takes the INITIAL population to double, in which case we need to find the population at time zero.
F(0) = 400 * log 4
= 400 * 0.60206 or approx. 241 individuals
then double this to get 482, which is exactly the number you got for six months of population growth.
Lets check:
482 = 400 (log 2t + 4)
1.205 = log (2t + 4)
10^1.205 = 2t + 4
16 = 2t + 4
12 = 2t
t = 6 months!