(a) Evaluate and interpret P(0).Which sentence below best describes P(0)?b) What percentage of households did not own a personal computer in 1997?c) In what year will the percentage of households that do not own a personal computer reach 25%? 91.4839KiThe logistic model P(t) =0 2229 represents the percentage of households that do not own a personal computer t years since 1985. Complete parts (a) - (c).1 +0.0386 e(a) Evaluate and interpret P(0).P(0) =%(Round to one decimal place as needed.)Which sentence below best describes P(0)?O A. P(0) is the percentage of households without a personal computer in 1985.O B. P(0) is the year all households had a personal computer.O C. P(0) is the percentage of households with a personal computer in 1985.O D. P(0) is the year no households had a personal computer.(b) What percentage of households did not own a personal computer in 1997?In 1997, % of households did not own a personal computer.(Round to one decimal place as needed.)(c) In what year will the percentage of households that do not own a personal computer reach 25%?During the year the percentage of households that do not own a personal computer will reach 25%.

(a) Evaluate and interpret P(0). Which sentence below best describes P(0)? b) What percentage of households did not own a personal computer in 1997? c) In what year will the percentage of households that do not own a personal computer reach 25%?

(a) Evaluate and interpret P(0). Which sentence below best describes P(0)? b) What percentage of households did not own a personal computer in 1997? c) In what year will the percentage of households that do not own a personal computer reach 25%?

College Algebra

1st Edition

ISBN:9781938168383

Author:Jay Abramson

Publisher:Jay Abramson

Chapter6: Exponential And Logarithmic Functions

Section6.8: Fitting Exponential Models To Data

Problem 2TI: Sales of a video game released in the year 2000 took off at first, but then steadily slowed as time...

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Sales of a video game released in the year 2000 took off at first, but then steadily slowed as time moved on. Table 4 shows the number of games sold, in thousands, from the years 20002010. a. Let x represent time in years starting with x=1 for the year 2000. Let y represent the number of games sold in thousands. Use logarithmic regression to fit a model to these data. b. If games continue to sell at this rate, how many games will sell in 2015? Round to the nearest thousand.
More on the Pacific Sardine This is a continuation of Example 5.1. In this exercise, we explore the Pacific sardine population further, using the model in Example 5.1. a. If the current level of the Pacific sardine population is 50,000 tons, how long will it take for the population to recover to the optimum growth level of 1.2milliontons? Suggestion: One way to solve this is to make a new logistic formula using K2.4, r0.338, and N(0)0.05. b. The value of r used in Example 5.1 ignores the effects of fishing. If fishing mortality is taken into account, then r drops to 0.215 per year with the carrying capacity still at 2.4milliontons. Answer the question in part a using this lower value of r. Note: The population estimate of 50,000 tons and the adjusted value of r are given in the paper by Murphy see footnote 3 on page 347. Murphy points out that factoring in the growth of the competing anchovy population makes the recovery times even longer, and he adds. "It is disconcerting to realize how slowly the population will recover to its level of maximum productivity ... even if fishing stops." Studies to fit a logistic model to the Pacific sardine population have yielded. N=241+239e0.338t where t is measured in years and N is measured in millions of tons of fish. Part 1 What is r for the Pacific sardine? Part 2 According to the logistic model, in the absence of limiting factors, what would be the annual percentage growth rate for the Pacific sardine? Part 3 What is the environmental carrying capacity K? Part 4 What is the optimum yield level? Part 5 Make a graph of N versus t. Part 6 At what time t should the population he harvested? Part 7 What portion of the graph is concave up? What portion is concave down?
Modeling Human Height with a Logistic Function A male child is 21inches long at birth and grows to an adult height of 73inches. In this exercise, we make a logistic model of his height as a function of age. a. Use the given information to find K and b for the logistic model. b. Suppose he reaches 95 of his adult height at age 16. Use this information and that from part a to find r. Suggestion: You will need to use either the crossing-graphs method or some algebra involving the logarithm. c. Make a logistic model for his height H, in inches, as a function of his age t, in years. d. According to the logistic model, at what age is he growing the fastest? e. Is your answer to part d consistent with your knowledge of how humans grow?
The fox population in a certain region has an annualgrowth rate of 9 per year. In the year 2012, therewere 23,900 fox counted in the area. What is the foxpopulation predicted to be in the year 2020 ?
What does the y -intercept on the graph of a logistic equation correspond to for a population modeled by that equation?
What is the carrying capacity for a population modeled by the logistic equation P(t)=250,0001+499e0.45t ? initial population for the model?
What is the y -intercept of the logistic growth model y=c1+aerx ? Show the steps for calculation. What does this point tell us about the population?
What situations are best modeled by a logistic equation? Give an example, and state a case for why the example is a good fit.