13. The population of a northern Michigan town was 4,500 people in 2010 and 7,200 people in 2015.a) Write a function of the form P(t) = ae" to model the population P(t) t years after 2010. Round b to three decimalplaces.b) Use the function from part a) to approximate the population of this town in 2024, Round to the nearest person.

Given: Population in 2010 = 4500 and Population in 2015 = 7200 (a) Write a function of the form P(t)…

Answered: 13. The population of a northern…

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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The number (in thousands) of women in the work force as function of the year is shown in the figure below. Calculate and interpret the following in your case study report. Evaluate f(1983) and f(2011) using the graph. Solve f(year) = 50,000,000 using the graph. Solve f(year) = 43,000,000 using the graph. Estimate f(2014) - f(1994) using the graph. What are the natural domain and range of this function?
Do question 39 please
Imagine that you are studying how the number of rabbits and chipmunks evolved between 1950 and 2000 in New York, You have collected historical data and have summarized it in the following graph: a) Find an expression for each species that helps you calculate the number of animals of each species between 1950 and 2000 as a function of the year. Use R as a symbol for rabbits, C as the symbol for chipmunks, and Y as the symbol for years. You will be finding two seperate equations. b) For which year was the population of rabbits approximately four times the population of the chipmunks? c) There is data that supports the hypothesis that linear trends observed between 1950 and 2000 will continue in the future. By which year will both populations be approximately the same?
A clock is hung on a wall so that the bottom of the clock is exactly 75 inches above the ground. The minute hand (the longest hand) is 7 inches long and touches the edge of the clock. Write a function h(t)that describes the height of the tip of the minute hand above the ground at any time, t. For ease, assume the scenario begins at noon. Recall: it takes 60 minutes for the minute hand to make a complete revolution around the clock.
3. A 10 Dirhem Coin is dropped from the top of the tallest building in the world (Burj Khalifa, in Dubai, UAE). Until the coin hits the ground, the height (in meters above ground) of the coint seconds after it has been dropped is modeled by the function h(t) = 828 – 4.9t. a. What is the height of the building? b. How long does it take for the coin to reach the ground? c. How fast is the coin falling as it hits the ground? d. How fast is the coin falling when it is halfway to the ground? e. What do your answers to parts c and d tell you about what seems to happen to the speed of the object as it falls? Does this fit with your intuition?
The triangular holes have a base of 3 inches and a height of h inches, and the other dimensions are also in inches. Find the shaded area as a function of h. 16
During Ricardo noticed an ink stain with a diameter of about 3 cm on the front of his teacher’s shirt. He then noticed that there was a pen in the pocket and that the ink blot was continuing to spread across the front of the teacher’s shirt. He estimated that the diameter of the ink blot seemed to be growing by about 0.5 cm every 2 minutes. a) Write an equation for the RADIUS, r, of the ink stain, as a function of time, t. Assume that t = 0 represents the time that Ricardo first noticed the ink stain. b) Write an equation showing the AREA, A, of the ink stain as a function of the time t. (Hint: It might help to first write A as a function of r. ) c) Draw a graph of the function A(t) for 10 minutes. d) At what time is the area of the ink stain about 25 square centimeter? Show how you answer this question. (i.e. ”I found it using desmos” is not sufficient)
The population of a Ukrainian village is currently 500. Based on the observed growth of the population in past years it is estimated that after 1 year the population will be 600. Similarly, it is estimated that after 2 and 3 years, the population of the village will be 720 and 864 respectively.Which function describes the relationship between year and the village population?
A cell phone plan charges $30 per month for unlimited call and text messages, however each gigabyte (GB) of data is charged at a rate of $10 per GB. Assume that fractional values of a GB are prorated according to this rate. If a user uses more than 15 GB of data during their monthly billing cycle, then they are not charged more than the cost for the first 15 GB. Write a piecewise-defined function that describes the amount a cell phone user will pay, C, as a function of the number of GB of data they use, d, over the course of a month. (You may enter the intervals using either interval notation or as an inequality. Do not include the dollar sign in any of your answers.) Provide your answer below: The first piece of C(d) is defined in the interval The second piece is defined in the interval
The U.S. population can be modeled by the function y=165.6x¹.345, where y is in thousands and x is the number of years after 1800. (a) What was the population in 1970, according to this model? (b) is the graph of this function concave up or concave down? What does this mean? (c) Use numerical or graphical methods to find when the model estimates the population was 94,150,000. (a) According to the model, the population in 1970 was thousands. (Round to the nearest integer as needed.)
8 Please give me the full solution and answer, Thank you
1. When you swim underwater, the pressure in your ears depends on the depth at which you are swimming. The formula p=0.43d relates the water pressure p, in pounds per square feet, to a depth of d feet. We can use this linear function to determine the pressure in your ears at a different depths. (a) If your depth is doubled, how did the pressure change? (b) Fill in the blank: i. If the depth is increasing, the pressure is ii. If the depth is decreasing, the pressure is

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