Solve the problem.
-According to a country's census, the population (to the nearest million) was 266 in Year 0 and 306 in Year 10. The projected population for Year 50 is 445. To construct a logistic model, both the growth and carrying capacity must be estimated.
(a) Estimate r by assuming that t = 0 corresponds to Year 0 and that the population between Year 0 and Year 10 is exponential; that is, the population is given by Round the value of r to four decimal places, if necessary.
(b) Write the solution to the logistic equation using the estimated value of r and use the projected value P(50) = 445 million to find an estimation for the value of the carrying capacity K. Round to the nearest million.

Question

Solve the problem.  
-According to a country's census, the population (to the nearest million) was 266 in Year 0 and 306 in Year 10. The projected population for Year 50 is 445. To construct a logistic model, both the growth and carrying capacity must be estimated.
(a) Estimate r by assuming that t = 0 corresponds to Year 0 and that the population between Year 0 and Year 10 is exponential; that is, the population is given by  Round the value of r to four decimal places, if necessary.
(b) Write the solution to the logistic equation using the estimated value of r and use the projected value P(50) = 445 million to find an estimation for the value of the carrying capacity K. Round to the nearest million.

Quizplus · Accepted Answer

The Answer of Solve the problem.  
-According to a country's census, the population (to the nearest million) was 266 in Year 0 and 306 in Year 10. The projected population for Year 50 is 445. To construct a logistic model, both the growth and carrying capacity must be estimated.
(a) Estimate r by assuming that t = 0 corresponds to Year 0 and that the population between Year 0 and Year 10 is exponential; that is, the population is given by  Round the value of r to four decimal places, if necessary.
(b) Write the solution to the logistic equation using the estimated value of r and use the projected value P(50) = 445 million to find an estimation for the value of the carrying capacity K. Round to the nearest million.

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