Answered

Welcome to Westonci.ca, the Q&A platform where your questions are met with detailed answers from experienced experts. Experience the convenience of finding accurate answers to your questions from knowledgeable professionals on our platform. Experience the ease of finding precise answers to your questions from a knowledgeable community of experts.

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 were added to the lake.Find the population size of the species after 4 years and the population size after 8 yearsRound your answers to the nearest whole number as necessary.

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 T class=

Sagot :

a) 223 fishes

b) 352 fishes

Explanation:[tex]\begin{gathered} \text{The given function:} \\ P(t)\text{ = }\frac{1200}{1+8e^{-0.15t}} \\ \\ We\text{ n}eed\text{ to find the }P(t)\text{ when t = 4 years and t = 8 years} \end{gathered}[/tex][tex]\begin{gathered} \text{when t = 4 years} \\ \text{substitute 4 for t in the given function} \\ P(t)\text{ = }\frac{1200}{1+8e^{-0.15(4)}} \\ P(t)\text{ = }\frac{1200}{1+4.3905}\text{= }\frac{1200}{5.3905} \\ P(t)\text{ = }222.61 \\ \\ To\text{ the nearest whole number, population size is 223 fishes} \end{gathered}[/tex][tex]\begin{gathered} \text{when t = 8 years} \\ P(t)\text{ = }\frac{1200}{1+8e^{-0.15(8)}} \\ P(t)\text{ =}\frac{1200}{1+2.4096}\text{ = }\frac{1200}{3.4096} \\ P(t)\text{ = }351.95 \\ \\ To\text{ the nearest whole number, population size is 352 fishes} \end{gathered}[/tex]

Thanks for using our service. We aim to provide the most accurate answers for all your queries. Visit us again for more insights. Thank you for choosing our platform. We're dedicated to providing the best answers for all your questions. Visit us again. We're here to help at Westonci.ca. Keep visiting for the best answers to your questions.