try again your answer is incorrect. population size after 7 years: your answer is incorrect. a species of…

try again your answer is incorrect. population size after 7 years: your answer is incorrect. a species of fish was added to a lake. the population size p(t) of this species can be modeled by the following function, where t is the number of years from the time the species was added to the lake. p(t)=1200 / (1 + 8e^(-0.26t)) find the population size of the species after 4 years and the population size after 7 years. round your answers to the nearest whole number as necessary. population size after 4 years: fish population size after 7 years: fish

try again your answer is incorrect. population size after 7 years: your answer is incorrect. a species of fish was added to a lake. the population size p(t) of this species can be modeled by the following function, where t is the number of years from the time the species was added to the lake. p(t)=1200 / (1 + 8e^(-0.26t)) find the population size of the species after 4 years and the population size after 7 years. round your answers to the nearest whole number as necessary. population size after 4 years: fish population size after 7 years: fish

Answer

Explanation:

Step1: Calculate population after 4 years

Substitute $t = 4$ into $P(t)=\frac{1200}{1 + 8e^{-0.26t}}$. $P(4)=\frac{1200}{1 + 8e^{-0.26\times4}}$ First calculate the exponent part: $-0.26\times4=-1.04$. Then $e^{-1.04}\approx0.353$. $8e^{-1.04}\approx8\times0.353 = 2.824$. $1+8e^{-1.04}\approx1 + 2.824=3.824$. $P(4)=\frac{1200}{3.824}\approx314$.

Step2: Calculate population after 7 years

Substitute $t = 7$ into $P(t)=\frac{1200}{1 + 8e^{-0.26t}}$. $P(7)=\frac{1200}{1 + 8e^{-0.26\times7}}$ First calculate the exponent part: $-0.26\times7=-1.82$. Then $e^{-1.82}\approx0.162$. $8e^{-1.82}\approx8\times0.162 = 1.296$. $1+8e^{-1.82}\approx1+1.296 = 2.296$. $P(7)=\frac{1200}{2.296}\approx522$.

Answer:

Population size after 4 years: 314 fish Population size after 7 years: 522 fish