Question #346105

2 As the biologist for a certain crocodile farm, you know that its carrying capacity is 20,000 crocodiles. You initially release 5000 crocodiles into the farm. After 6 weeks, the crocodile population has increased to 7500. In how many weeks will the population reach 10,000? In how many weeks will the population reach 20,000^ prime


1
Expert's answer
2022-05-30T14:57:55-0400
N(t)=N(0)ektN(t)=N(0)e^{kt}

Given N(0)=5000N(0)=5000


7500=5000ek(6)7500=5000e^{k(6)}

6k=ln1.56k=\ln 1.5

k=16ln1.5k=\dfrac{1}{6}\ln 1.5

N(t)=5000(1.5)t/6N(t)=5000(1.5)^{t/6}

a)


10000=5000(1.5)t/610000=5000(1.5)^{t/6}

(1.5)t/6=2(1.5)^{t/6}=2

t6ln1.5=ln2\dfrac{t}{6}\ln1.5=\ln2

t=6ln2ln1.5t=\dfrac{6\ln 2}{\ln1.5}

t=10.257 weekst=10.257\ weeks

b)


20000=5000(1.5)t/620000=5000(1.5)^{t/6}

(1.5)t/6=4(1.5)^{t/6}=4

t6ln1.5=ln4\dfrac{t}{6}\ln1.5=\ln4

t=12ln2ln1.5t=\dfrac{12\ln 2}{\ln1.5}

t=20.514 weekst=20.514\ weeks




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