Math Problem Statement

User responses cleared Homework:HW SECTION 9.5 Question 8, 9.5.38 Part 1 of 7 HW Score: 89.29%, 7.14 of 8 points Points: 0.14 of 1

Skip to Main content Question 1 Question 2 Question 3 Question 4 Question 5 Question 6 Question 7 Question 8 Question content area top Part 1 A​ nation's population​ (to the nearest​ million) was 281 million in 2000 and 310 in 2010. It is projected that the population in 2050 will be 437 million. To construct a logistic​ model, both the growth rate and the carrying capacity must be estimated. There are several ways to estimate these parameters. Use parts​ (a) through​ (f) to use one approach. Question content area bottom Part 1 a. Assume that tequals0 corresponds to 2000 and that the population growth is exponential for the first ten​ years; that​ is, between 2000 and​ 2010, the population is given by Upper P left parenthesis t right parenthesis equals Upper P left parenthesis 0 right parenthesis e Superscript rt. Estimate the growth rate r using this assumption. requals    enter your response here ​(Round to five decimal places as​ needed.) r(Round to five decimal places as needed.)P(t)K(Type an integer or decimal rounded to the nearest hundredth as needed.)The population will reach 95% of the carrying capacity in the year(Type an integer or decimal rounded to the nearest hundredth as needed.)K(Type an integer or decimal rounded to the nearest hundredth as needed.)K(Type an integer or decimal rounded to the nearest hundredth as needed.)Choose the correct response below.r(Round to five decimal places as needed.) Get more help

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Math Problem Analysis

Mathematical Concepts

Exponential Growth
Logistic Growth
Population Modeling

Formulas

P(t) = P(0) e^{rt}
r = (1/t) ln(P(t)/P(0))

Theorems

Exponential Growth Model
Logarithmic Properties

Suitable Grade Level

Grades 10-12