8-36. review The graph of an exponential function y = ab* +k passes through (3, 7.5) and (4, 6.25). It also has an asymptote at y=5. a. What is the equation of the function?
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A: Topic:- function
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- We opened this section with a study showing that late in the semester, procrastinating students reported more symptoms of physical illness than their nonprocrastinating peers.a. At the beginning of the semester, procrastinators reported an average of 0.8 symptoms, increasing at a rate of 0.45 symptoms per week. Write a function that models the average number of symptoms after x weeks.b. At the beginning of the semester, nonprocrastinators reported an average of 2.6 symptoms, increasing at a rate of 0.15 symptoms per week. Write a function that models the average number of symptoms after x weeks.c. By which week in the semester did both groups report the same number of symptoms of physical illness? For that week, how many symptoms were reported by each group?How is this shown in Figure.The bar graph shows the number of fatal vehicle crashes per 100 million miles driven for drivers of various age groups.25-year-old drivers areinvolved in 4.1 fatal crashes per 100 million miles driven. Thus, when a group of 25-year-old Americans have driven a total of 100 million miles, approximately 4 have been in accidents in which someone died.The number of fatal vehicle crashes per 100 million miles, y, for drivers of age x can be modeled by the formulay = 0.013x2 - 1.19x + 28.24.Use the formula above and the bar graph.What age groups are expected to be involved in 10 fatal crashes per 100 million miles driven? How well does the formula model the trend in the actual data shown by the bar graph?An fruit grower knows from previous experience and careful data analysis that if the fruit on a specific kind of tree is harvested at this time of year, each tree will yield, on average, 130 pounds, and will sell for $0.6 per pound. However, for each additional week the harvest is delayed (up to a point), the yield per tree will increase by 7 pounds, while the price per pound will decrease by $0.02.A) How many weeks should the grower wait before harvesting the apples in order to maximize the sales revenue per tree? (Round your answer to the nearest tenth of a week.)Answer: (rounded to the nearest tenth)B) Use your answer in part A to find the actual maximum revenue that can be expected. (Round your answer to the nearest dollar.)Answer: dollars (rounded to the nearest dollar)
- Plot the percentage of machines not running as a function of the service factor for a population of 20 machines with exponential arrivals and services (a) if a single channel is employed and (b) if two channels are employed.Life Expectancy at 65 Using data for selectedyears from 1950 and projected to 2050, the functiony = 0.077x + 13.827 gives the life expectancy atage 65, with y equal to the number of additional yearsof expected life at age 65 and x equal to the numberof years after 1950.a. Why is this a linear function?b. Find and interpret the slope of the graph of thisfunction.(Source: Social Security Administration)The price of 1 gallon of unleaded gasoline at the pump dropped to $2.19 on January 1, 2015, and continued to fall at the rate of 4 cents per month for the next 9 months. Express the price of 1 gallon of unleaded gasoline as a function of time for the period starting January 1, 2015. What was the price of 15 gallons of gasoline on April 1, 2015? On September 1, 2015?
- A plant grows quickly at first , remains at a constant height during a dry spell , then grows at a steady pace . graph time on the x-axis and the height of the plant on the y-axisWhen the U.S. Environmental Protection Agency found a certain company emitting ozone-depleting substances from refrigeration equipment, it fined the company $600,000, plus $50,000 per month until the company complied with federal emission regulations. Express the total fine as a function of the number of months, x, the company continued to violate the federal regulations.Go to the St. Louis Federal Reserve FRED databaseand find data on the M1 money supply (M1SL) andthe 10-year treasury bond rate (GS10). Add the twoseries into a single graph by using the “Add DataSeries” feature. Transform the M1 money supplyvariable into the M1 growth rate by adjusting theunits for the M1 money supply to “Percent Changefrom Year Ago.”a. In general, how have the growth rate of theM1 money supply and the 10-year treasurybond rate behaved during recessions andduring expansionary periods since the year2000?b. In general, is there an obvious, stable relationship between money growth and the10-year interest rate since the year 2000?c. Compare the money growth rate and the10-year interest rate for the most recentmonth available to the rates for January2000. How do the rates compare?
- the topic is Elimination of Arbitrary Constants by Isolation of ConstantsScientists in Malaysia have collected data revealing that there is a linear relationship between the length (snout to vent) of the beaked sea snake and the length of its catfish prey such that l(x) = 2.41 + 0.12x, where x is the snout-vent length (cm) of the snake and l(x) is the predicted length (cm) of the catfish. Source: Biotropica. a. Use the function above to estimate the size of catfish that a snake which has a snout-vent length of 70 cm will choose for prey. b. Calculate the derivative of this function and interpret the results.The initial weight of a container is 6.2 pounds. As water is added to the container, the weight increases at a rate of 0.6 pounds per minute. Which function models the weight of the container as a function of time?