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**Unformatted text preview: **Section 8.2 Exponential Functions 783 Version: Fall 2007 8.2 Exercises 1. The current population of Fortuna is 10,000 hearty souls. It is known that the population is growing at a rate of 4% per year. Assuming this rate remains constant, perform each of the following tasks. a. Set up an equation that models the population P ( t ) as a function of time t . b. Use the model in the previous part to predict the population 40 years from now. c. Use your calculator to sketch the graph of the population over the next 40 years. 2. The population of the town of Imag- ination currently numbers 12,000 people. It is known that the population is grow- ing at a rate of 6% per year. Assuming this rate remains constant, perform each of the following tasks. a. Set up an equation that models the population P ( t ) as a function of time t . b. Use the model in the previous part to predict the population 30 years from now. c. Use your calculator to sketch the graph of the population over the next 30 years. 3. The population of the town of De- spairia currently numbers 15,000 individ- uals. It is known that the population is decaying at a rate of 5% per year. As- suming this rate remains constant, per- form each of the following tasks. Copyrighted material. See: http://msenux.redwoods.edu/IntAlgText/ 1 a. Set up an equation that models the population P ( t ) as a function of time t . b. Use the model in the previous part to predict the population 50 years from now. c. Use your calculator to sketch the graph of the population over the next 50 years. 4. The population of the town of Hope- less currently numbers 25,000 individu- als. It is known that the population is decaying at a rate of 6% per year. As- suming this rate remains constant, per- form each of the following tasks. a. Set up an equation that models the population P ( t ) as a function of time t . b. Use the model in the previous part to predict the population 40 years from now. c. Use your calculator to sketch the graph of the population over the next 40 years. In Exercises 5- 12 , perform each of the following tasks for the given function. a. Find the y-intercept of the graph of the function. Also, use your calcula- tor to find two points on the graph to the right of the y-axis, and two points to the left. b. Using your five points from (a) as a guide, set up a coordinate system on graph paper. Choose and label ap- propriate scales for each axis. Plot the five points, and any additional points you feel are necessary to dis- 784 Chapter 8 Exponential and Logarithmic Functions Version: Fall 2007 cern the shape of the graph....

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