Concept explainers
For the following exercises, consider this scenario: For each year t, the population of a forest oftrees is representedby the
9. Which forest’s population is growing at a faster rate?
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Algebra and Trigonometry
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- For the following exercises, consider this scenario: For each year t , the population of a forest of trees is represented by the function A(t)=115(1.025)t. In a neighboring forest, the population of the same type of tree is represented by the function B(t)=82(1.029)t. (Round answers to the nearest whole number.) Assuming the population growth models continue to represent the growth of the forests, which forest will have a greater number of trees after 100 years? By how many?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, consider this scenario: For each year t , the population of a forest of trees is represented by the function A(t)=115(1.025)t. In a neighboring forest, the population of the same type of tree is represented by the function B(t)=82(1.029)t. (Round answers to the nearest whole number.) Discuss the above results from the previous four exercises. Assuming the population growth models continue to represent the growth of the forests, which forest will have the greater number of trees in the long run? Why? What are some factors that might in?uence the long-term validity of the exponential growth model?arrow_forward
- For 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_forwardFor the following exercises, solve for the desired quantity. 60. A guitar factory has a cost of production C(x)=75x+50,000 . If the company needs to break even after 150 units sold, at what price should they sell each guitar? Round up to the nearest dollar,and write the revenue function.arrow_forwardFor 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 2005 until 2010. In 2005, 12,025 people were afflicted. When will the output reach 0?arrow_forward
- For the following exercises, use this scenario: A tumor is injected with 0.5 grams of Iodine-125, which has a decay rate of 1.15% per day. To the nearest day, how long will it take for half of the Iodine-125 to decay?arrow_forwardFor the following exercises, consider this scenario: A town has an initial population of 75,000. It grows at a constantrate of 2,500 per year for 5 years. If the function P is graphed, find and interpret thex-and y-intercepts.arrow_forwardFor 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 2005 until 2010. In 2005, 12,025 people were afflicted. If the function C is graphed, find and interpret the x-and y-intercepts.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 turkey is taken out of the oven with an internal temperature of 165° Fahrenheit and is allowed to cool in a 75° F room. After half an hour, the internal temperature of the turkey is 145° F. To the nearest minute, how long will it take the turkey to cool to 110° F?arrow_forwardFor the following exercises, solve the application problem. 48.The volume V of an ideal gas varies directly with thetemperature T and inversely with the pressure P.A cylinder contains oxygen at a temperature of310 degrees K and a pressure of 18 atmospheres in avolume of 120 liters. Find the pressure if the volumeis decreased to 100 liters and the temperature isincreased to 320 degrees K.arrow_forward