In 1997, 1500 runners entered a marathon in Joppetown U.S.A. In 2003, 18,000 runners entered the race. Because of the limited number of facilities, the carrying capacity for the number of racers is 58,500. The number of racers atany time, t, in years, can be modeled by the logistic function P(t) =C.Complete parts a) through d) below.%3D1+Be kta) What is the value of C?C =b) Find B.B =c) Find k.k =(Type an exact answer in simplified form. Use integers or fractions for any numbers in the expression.)d) In what year should at least 48,500 runners be expected to run in the race?In theyear(Do not round until the final answer Then round un to the nearest whole pumber)

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In 1997, 1500 runners entered a marathon in Joppetown U.S.A. In 2003, 18,000 runners entered the race. Because of the limited number of facilities, the carrying capacity for the number of racers is 58,500. The number of racers at any time, t, in years, can be modeled by the logistic function P(t) = Complete parts a) through d) below. 1+Bekt a) What is the value of C? b) Find B B=D c) Find k. (Type an exact answer in simplified form. Use integers or fractions for any numbers in the expression.)

In 1997, 1500 runners entered a marathon in Joppetown U.S.A. In 2003, 18,000 runners entered the race. Because of the limited number of facilities, the carrying capacity for the number of racers is 58,500. The number of racers at any time, t, in years, can be modeled by the logistic function P(t) = Complete parts a) through d) below. 1+Bekt a) What is the value of C? b) Find B B=D c) Find k. (Type an exact answer in simplified form. Use integers or fractions for any numbers in the expression.)

Algebra and Trigonometry (6th Edition)

6th Edition

ISBN:9780134463216

Author:Robert F. Blitzer

Publisher:Robert F. Blitzer

ChapterP: Prerequisites: Fundamental Concepts Of Algebra

Section: Chapter Questions

Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...

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Concept explainers

Limits

When it comes to calculus, limits are considered to be a very important topic of discussion. The main importance of limit lies in expressing the value of a function as it gets closer to a certain value. Also, limits can help you to understand other topics, such as continuity and differentiability better. In a broader sense, every calculus notion is a limit. Other branches of calculus have also been derived from limits.

Question

In 1997, 1500 runners entered a marathon in Joppetown U.S.A. In 2003, 18,000 runners entered the race. Because of the limited number of facilities, the carrying capacity for the number of racers is 58,500. The number of racers at
any time, t, in years, can be modeled by the logistic function P(t) =
C
.Complete parts a) through d) below.
%3D
1+Be kt
a) What is the value of C?
C =
b) Find B.
B =
c) Find k.
k =
(Type an exact answer in simplified form. Use integers or fractions for any numbers in the expression.)
d) In what year should at least 48,500 runners be expected to run in the race?
In the
year
(Do not round until the final answer Then round un to the nearest whole pumber)

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