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- 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 2005 until 2010. In 2005, 12,025 people were afflicted. When will the output reach 0?The rate of change of an autocatalytic chemical reaction is kQxkx2 where Q is the amount of the original substance, x is the amount of substance formed, and k is a constant of proportionality. Factor the expression.For the following exercises, solve for the desired quantity. 58. A cell phone factory has a cost of production C(x)=150x+10,000 and a revenue function R(x)=200x . What is the break-even point?
- Using Figure 7, solve f(x)=1 .For 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?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?
- For 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. Find a reasonable domain and range for the function P.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.For the following exercises, use the values listed in Table 1. 29. Solve the equation F(x)=5 .
- Find the average rate of change of f(x)=x2+2x8 on the interval [5,a] in simplest forms in terms ofa.For 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.For the following exercises, refer to Table 11. Use the intersect feature to find the value of x for which the model reaches half its carrying capacity.