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)

Since you have posted a question with multiple sub-parts, we will solve first three subparts for…

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,...

See similar textbooks

Related questions

Q: 7. If log n² = 5, determine the value of log b³. Use laws of logarithms.

Q: The table lists the number of species of birds on islands of various sizes. Find values for a and b…

A: Given query is to find the value of a and b.

Q: The expected life span of people in a country for certain birth years is given in the table.…

Q: The logistic model P(t) = OA. ⒸU. FU/ i5 te pervemage vi fiusenvius without a personal computer in…

A: The given equation isWhere t is the number of years after 1986 and P is the percentage of households…

Q: Use logarithms to transform the non-linear model y= 6(3)2 into a linear model. Express your final…

A: Given

Q: a) log, 6 b) log, 3

Q: 14. Set up and solve an equation to evaluate log, ().

A: Given logg13=?we know thatlogabc=c logablogambh=hmlogab , logaa=1

Q: If f(x)=√x+7 and h(x) = 6 -, find f(x) + h(x). X

Q: a)Determine the price of the home after 12 years. b)What type of function does the data represent?…

Q: for 20 units. The third scale took 90 hours to produce. Based on past experience, the learning rate…

A: The given information is, learning rate = r = 0.88 So, b can be calculated as:

Q: 4. a) Can you punch the following into your calculator and solve? Why or why not? log,(512) b) Based…

A: Yes, calculation of logarithm in calculator can be performer easily we have to use ln if log is…

Q: Given the functions ) - logz and )-2-x which of the following is most likely the graph of-Aet?

Q: 1. What is log,, 100? What about log,00 10? 2. What is log, 4? What about log, 2? 3. Express b as a…

A: values=?

Q: III. EVALUATION of LOGARITHMIC FUNCTIONS. Solve and evaluate the following Logarithmic Functions. 1.…

Q: 12.xe y = V3x + 2

Q: You are considered the first generation, your parents are considered the second generation, your…

A: Hi, thank you for the question. Since you have posted a question with multiple subparts, as per our…

Q: 7. The base of the natural logarithm system is:

A: Natural logarithm is logarithm with base e (exponential base), mostly written as

Q: The length of a stalactite (in mm) has been measured at the beginning of every fourth year since the…

Q: Write 3log, 10+÷log, 4 as a single logarithm.

A: The given expression is: 3log510+12log54

Q: 1 a) log 16 X = -4 c) log, 2x+log, 5=-1 b) log, 2 = x d) x = log, 625

Q: Given the function Ax) = logx determine the value of af'(23)- O 1023 23 2.3 230

Q: 9. log,x = -5

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)

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

This is a popular solution!

SEE SOLUTION Check out a sample Q&A here

Step 1

VIEW

Step 2

VIEW

Step 3

VIEW

Trending now

This is a popular solution!

Step by step

Solved in 3 steps

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

$Limits and Continuity$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, algebra and related others by exploring similar questions and additional content below.

Similar questions

1. Evaluate the following. Final answer is in exact form, no decimals.
v. Use log, 2 0.356, log,3 = 0.565, and log,5 0.827 to approximate the value of the given logarithm. 11.) log, 150
6.) Use the acidity model give by pH = - log [H•]. where acidity (pH) is a measure of the hydrogen ion concentration [H] (measured in moles of hydrogen per liter) of a solution. a) Find the pH if [H] = 2.3 x 10-s, (Round to the nearest tenth.) am od ne 810S or 2105 moni VM b99weldmuT to (ahnsauony n) nouelugog sri b) Compute [H] for a solution in which the pH = 4.9. (Round to eight decimal places.)W La
An experiment involves dropping a ball and recording the distance it falls (y) for different times (x) after it was released. Construct a scatterplot and identify the mathematical model that best fits the given data. Assume that the model is to be used only for the scope of the given data, and consider only linear, quadratic, logarithmic, exponential, and power models. Time (seconds) Distance (meters) 0.5 1 1.2 4.8 1.5 10.7 2 18.5 2.5 3 28 38.9 Choose the correct scatterplot below. OA. B. Q 50- 50- 40- ° 40-0 a 30- 20- 20- 10- 0- 2 G 10- 0- 0 1 2 C. O D. Q 50- 40- 30- 20- 10- о 0 1 2 3 Q 50- 40- Q 30- 20- ° G 10- ° ° 0- 0 1 2 What is the equation of the best model? Select the correct choice below and fill in the answer boxes to complete your choice. Enter only nonzero values. (Type integers or decimals rounded to three decimal places as needed.) OA. y= OB. y= + Inx OC. y= OD. y= OE. y= x + x+ о
Answer ASAP and show work please, thank uu