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For the following exercises, use a graphing calculator and this scenario: the population of a fish farm in t years is modeled by the equation
What is the initial population of fish?
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- 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_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_forwardThe population of a culture of bacteria is modeled by the logistic equation P(t)=14,2501+29e0.62t where t is inarrow_forward
- Rachel invests $15,000 at age 25. She hopes the investments will be worth when she turns 40. If the interest compounds continuously, approximately what rate of growth will she need to achieve her goal?arrow_forwardFor the following exercises, use this scenario: A doctor prescribes 125 milligrams of a therapeutic drug that decays by about 30% each hour. To the nearest hour, what is the half-life of the drug?arrow_forwardFor the following exercises, use this scenario: A doctor prescribes 300 milligrams of a therapeutic drug that decays by about 17 each hour. To the nearest minute, what is the half-life of the drug?arrow_forward
- Jerome invests $18,000 at age 17. He hopes the investments will be worth $30,000 when he turns 26. If the interest compounds continuously, approximately what rate of growth will he need to achieve his goal? Is that a reasonable expectation?arrow_forwardFor 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_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_forward
- The 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_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. When will the output reached 100,000?arrow_forwardFor the following exercises, determine whether the equation represents continuous growth, continuous decay, or neither. Explain. Suppose an investment account is opened with an initial deposit of 12,000 earning 7.2 interest compounded continuously. How much will the account be worth after 30 years?arrow_forward
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