65. Population growth. Before 1859, rabbits did not existin Australia. That year, a settler released 24 rabbits intothe wild. Without natural predators, the growth of theAustralian rabbit population can be modeled by the un-inhibited growth model dP/dt = kP, where P(t) is thepopulation of rabbits t years after 1859. (Source: wwwdpi.vic.gov.au/agriculture.)a) When the rabbit population was estimated to be8900, its rate of growth was about 2630 rabbitsper year. Use this information to find k, and thenfind the particular solution of the differentialequation.b) Find the rabbit population in 1900 (t = 41) and therate at which it was increasing in that year.c) Without using a calculator, find P'(41)/P(41).

(a) Determine the value for k from the given differential equation. P=8900,…

Answered: 65. Population growth. Before 1859,…

Calculus: Early Transcendentals

8th Edition

ISBN:9781285741550

Author:James Stewart

Publisher:James Stewart

Chapter1: Functions And Models

Section: Chapter Questions

Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...

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solve part d
4. The national debt has increased over the last 20 year. Compare quadratic and exponential models. Which model seems more likely to represent the data set over time? Year U.S. National Debt (in trillions) 2000 5.7 2005 7.9 2010 13.6 2015 18.2 2017 20.2 2018 21.5 2021 26.9
ul T-Mobile 12:02 AM 100% 4 GEOVANNY ENRIQ... Name Date Per. Situations to Equations Homework Write an equation in y = mx + b form to describe each situation. Identify the starting point (initial value). That's b. Identify the growth. This one will often say ". o Is the growth positive or negative? • You can write your equation as y = mx + b or y = b + mx . per ". That's mx. mx = -27x b = 124 EXAMPLE: A store's sales of music CDs has decreased by 27 per year. There were 124 CDs sold in the first year. y = -27x + 124 1. A Norfolk pine is 18 inches tall and grows at a rate of 1.5 feet per year. 2. An airplane at an altitude of 3000 feet descends at a rate of 500 feet per mile. 3. An overweight Siamese cat weighs 20 pounds, and is on a diet to lose 1 pound per month. 4. An online store charges $3 per order plus $0.99 per book for shipping. 5. You have saved $50 toward the cost of a new television. You plan to save $5 more each week. 6. A rental company charges $8 per hour for a mountain…
4 The data collected by a biologist showing the growth of a colony of bacteria at the end of cach hour are displayed in the table below. Time bour, Population () 250 330 580 800 1650 3000 3. Write an exponential regression equation to model these data. Round all values to the nearest thousandth. Assuming this trend continues, use this equation to estimate, to the nearest fen, the number of bacteria in the colony at the end of 7 hours.
8
9. A certain bacteria population triples each minute. Suppose you begin with a single bacteria cell. a. Create a table of values to show the population of bacteria at the end of each minute for the first 5 minutes of growth. b. Graph the data from your table using the desmos graphing calculator. (insert below). c. Is the population of bacteria growing linearly or exponentially? Explain.
Determine whether the following scenarios are linear or exponential. As summer approaches, I noticed that for every increase in 5 degrees, the number of people I see at the pool increases by about 3. The amount of Francium,a radioactive element, decays by about 3.1% every minute. The number of flu cases increases by about 1.6% per month during flu season. Based on Mrs. Olivet's Test 4 results, students tended to score about 4 more points on their test for every hour they studied. The percentage of the population that has been vaccinated for COVID-19 increased by about 0.25 percentage points every day in January. The population of bugs in Monica's walls decreased by 80% every week while the exterminator was treating her home. During a rainstorm the reading from the rain gauge increased by a quarter inch every hour. Selene didn't want her parents to notice she was stealing candy from the jar, so every day she only ate 1/8 of what was left. While writing an essay, Carson writes 7…
Can I please get some help. Thank you!
B: Would the graph of y= 1.5x show exponential growth or exponcntial decay?
A new car costs $27, 000 depreciates to 80% of its value in 2 years. Round all answers to 2 decimal places, where necessary. a. Assume that the depreciation is linear. What is the linear function that models the value of this car t years after purchase? f(t) = Preview b. Assume that the value of the car is given by an exponential function Aekt, where A is the initial price of the car. Find the value of the constant k. Answer exactly. k = Preview c. For the linear model used in part (a), find the value of the car 6 years after the purchase, then do the same for the exponential model used in part (b). Round your answer to 2 decimal places. Linear after 6 years: $ Exponential after 6 years: $
Consider the plot of the total number E of Ebola cases in West Africa reported to the Centers for Disease Control and Prevention from April 1, 2014, through December 1, 2015. D +|+|||||||||||||||| ► Ebola Cases in West Africa E = A logistic fit for these data is given by 27,841.42 1 + 134.65-0.646 where t is the time in months since April 1, 2014. Below, we have added the graph of this model. +-+|||||||||||||||||| ► Logistic Graph Added (a) Does the first plot, "Ebola Cases in West Africa," show a continuing epidemic or a health crisis that is under control by December 2015? Because the data points appear to be [leveling off ✔✔✔, they show a health crisis that is under control (b) According to the model, what was the total number of cases when the disease was spreading at the fastest rate? Round your answer to the nearest whole number. 27021.61 x cases (c) Use the crossing-graphs method to determine when the disease was growing at the fastest rate. Round your answer, in months after…
6. From 1790 to 1860, U.S. population grew rapidly (see the table). Let f(t) be the population t years after 1790. a) Create a scattergram for the data on your Graphing Calculator. b) Based on your scattergram, what appears more appropriate, a linear model, or an exponential model? Explain Year 1790 1800 1810 1820 1830 1840 1850 1860 d) What is the base? What does it tell us about the rate of population growth? Population (millions) 3.9 5.3 7.2 9.6 12.9 17.1 23.2 31.4 c) Use ExpReg on your GC to find an equation to model the situation. Write your answer using function notation. Round using 6 decimal places.

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