Question

A species of fish was added to a lake. The population size P(t) of this species can be modeled by the following exponential function:P(t)=1500/(1+7e^-0.4t)where t is the number of years from the time the species was added to the lake.Find the initial population size of the species and the population size after 9 years. Round your answers to the nearest whole number as necessary.

Answer 1

Answer:

a) 188 fishes

b) 1259 fishes

Step-by-step explanation:

See it in the pic.

Answer 2

Initial population size is 188 and after 9 years we get 1259 fishes.

We have given that the function

$P(t)=\frac{1500}{1+7e^(-0.04t)}$

Where t is the number of years from the time the species was added to the lake.

We have to find the initial population size of the species and the population size after 9 years.

where p(0) is the population size of species and p(9) is the population size after 9 years.

Therefore we have the given function is at t=0

$P(0)=\frac{1500}{1+7e^(-0.04(0)))}=\frac{1500}{1+07e^0} \\=\frac{1500}{1+7} \\=\frac{1500}{8} \\=187.5\\=188$

at t=9 we have

$P(9)=\frac{1500}{1+7ex^{-0.4(9)} }\\=\frac{1500}{1+7e^{-3.6} } \\=\frac{1500}{1.191}\\ =1259.16\\=1259 fishes$

Therefore after 9 years we get 1259 fishes.

To learn more about the growth and decay visit:

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