Concept explainers
For the following exercises, use this scenario: The population P of a koi pond over x months is modeled by the
Graph the population model to show the population over a span of 3 years.
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College Algebra
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Algebra and Trigonometry
- For the following exercise, consider this scenario: In 2004, a school population was 1,700. By 2012 the population had grown to 2,500. Assume the population is changing linearly. a. How much did the population grow between the year 2004 and 2012? b. What is the average population growth per year? c. Find an equation for the population, P, of the school t years after 2004.arrow_forwardThe population of a lake of fish is modeled by the logistic equation P(t)=16,1201+25e0.75t, where t is time inyears. To the unrest hundredth, how manyyears will it take the lake to reach 80% of its carrying capacity?For the following exercises, use a graphing utility to create a scatter diagram of the data given in the table.Observe the shape of the scatter diagram to determine whether the data is best described by an exponential,logarithmic, or logistic model. Then use the appropriate regression feature to find an equation that models thedata. When necessary, round values to five decimal places.arrow_forwardHector invests $10,000 at age 21. He hopes the investments will be worth when he turns 50. If the interest compounds continuously, approximately what rate of growth Will he need to achieve his goal?arrow_forward
- For the following exercises, determine whether the equation represents continuous growth, continuous decay, or neither. Explain. y=2.25(e)2tarrow_forwardFor the following exercises, refer to Table 11. Use the LOGISTIC regression option to find a logistic growth model of the form y=c1+aebx that best fits the data in the table.arrow_forwardThe population P (in millions) of Texas from 2001 through 2014 can be approximated by the model P=20.913e0.0184t, where t represents the year, with t=1 corresponding to 2001. According to this model, when will the population reach 32 million?arrow_forward
- For the following exercises, consider this scenario: The number of people afflicted with the common cold in the winter months steadily decreased by 205 each year from 2.005 until 2010. In 2005, 12,025 people were afflicted. Find the linear function that models the number of people in?icted with the common cold, C, as a function of the year, t.arrow_forwardFor the following exercises, use this scenario: A doctor prescribes 125 milligrams of a therapeutic drug that decays by about 30% each hour. Using the model found in the previous exercise, find f (10) and interpret the result. Round to the nearest hundredth.arrow_forwardUse the result from the previous exercise to graph the logistic model P(t)=201+4e0.5t along with its inverse on the same axis. What are the intercepts and asymptotes of each function?arrow_forward
- For the following exercises, use the graph in Figure 3, showing the profit, y, in thousands of dollars, of a company in a given year, x, where x represents years since 1980. In 2004, a school population was 1250. By 2012 the population had dropped to 875. Assume the population is changing linearly. a. How much did the population drop between the year 2004 and 2012? b. What is the average population decline per year? c. Find an equation for the population, P, of the school t years after 2004.arrow_forwardRefer to the previous exercise. Suppose the lightmeter on a camera indicates an EI of 2 , and thedesired exposure time is 16 seconds. What should thef-stop setting be?arrow_forwardFor the following exercises, consider this scenario: A town has an initial population of 75,000. It grows at a constant rate of 2,500 per year for 5 years. What is the output in the year 12 years from the onset of the model?arrow_forward
- Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:Cengage