The value of a brand new car is $27,000 and the value depreciates 19% every year. Write a function to represent the value of the car after t years, where the monthly rate of change can be found from a constant in the function. Round all coefficients in the function to four decimal places. Also, determine the percentage rate of change per month, to the nearest hundredth of a percent. Function: f(t)
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- An antique table increases in value according to the function v(x)=550(1.05)x dollars, where x is the number of years after1980 . a. How much was the table worth in 1980 ? b. If the pattern indicated by the function remains valid, what was the value of the table in 1995 ? c. Use a table or a graph to estimate the year when this table will reach double its 1980 value.An antique table increases in value according to the function v(x)=950(1.07)x dollars, where x is the number of years after 1980. a. How much was the table worth in 1980? b. If the pattern indicated by the function remains valid, what was the value of the table in 1990? c. Use a table or a graph to estimate the year when this table will reach double its 1980 value.Gordon also decides to sell candy at school by the pound. The graph below displays the amount of money he can earn as a function, G, of how many pounds he sells. Gordon sell 25 pieces of candy, how much profit will he earn?
- The bar graph shows your chances of surviving to various ages once you reach 60.The functions f(x) = -2.9x + 286 and g(x) = 0.01x2 - 4.9x + 370 model the chance, as a percent, that a 60-year-old will survive to age x. a. Find and interpret f(90). b. Find and interpret g(90). c. Which function serves as a better model for the chance of surviving to age 90?The amount of caffeine in the bloodstream decreases by 27% every hour. A cup of coffee contains 97 mg of caffeine. Define a function, ff that gives the amount of caffeine remaining in the blood stream tt hours after the coffee was consumed. How many hours will it take for the amount of caffeine to reach half of the amount in the initial cup of coffee? hours A double shot of espresso contains 130 mg of caffeine. Define a function, g, that gives the amount of caffeine remaining in the blood stream x hours after the espresso was consumed. How many hours will it take for the amount of caffeine to reach half of the amount in the initial espresso? hours A can of Rock Star energy drink has 180 mg of caffeine in it. How long after you consume the Rock Star will the caffeine in your blood stream decrease to 90 mg?The amount of caffeine in the bloodstream decreases by 26% every hour. A cup of coffee contains 94 mg of caffeine. Define a function, f that gives the amount of caffeine remaining in the blood stream t hours after the coffee was consumed. How many hours will it take for the amount of caffeine to reach half of the amount in the initial cup of coffee? hours A double shot of espresso contains 126 mg of caffeine. Define a function, g , that gives the amount of caffeine remaining in the blood stream x hours after the espresso was consumed. How many hours will it take for the amount of caffeine to reach half of the amount in the initial espresso? hours A can of Rock Star energy drink has 180 mg of caffeine in it. How long after you consume the Rock Star will the caffeine in your blood stream decrease to 90 mg? hours True or False: The number of hours it takes for the amount of caffeine in your body to reach half of the amount initially in your body depends on the…
- The amount of caffeine in the bloodstream decreases by 24% every hour. A cup of coffee contains 98 mg of caffeine. Define a function, f that gives the amount of caffeine remaining in the blood stream t hours after the coffee was consumed. How many hours will it take for the amount of caffeine to reach half of the amount in the initial cup of coffee? hours A double shot of espresso contains 120 mg of caffeine. Define a function, g, that gives the amount of caffeine remaining in the blood stream x hours after the espresso was consumed. How many hours will it take for the amount of caffeine to reach half of the amount in the initial espresso? hours A can of Rock Star energy drink has 160 mg of caffeine in it. How long after you consume the Rock Star will the caffeine in your blood stream decrease to 80 mg?The bar graph shows your chances of surviving to various ages once you reach 60. The functions f(x) = -2.9x + 286 and g(x) = 0.01x2 - 4.9x + 370model the chance, as a percent, that a 60-year-old will survive to age x. Solve; a. Find and interpret f(70). b. Find and interpret g(70). c. Which function serves as a better model for the chance of surviving to age 70?The rise of digital music and the improvement to the DVD format are part of the reasons why the average selling price of standalone DVD recorderes will drop in the coming years. The function below gives the projected average selling price (in dollars) of standalone DVD recorders in year t, where t =0 corresponds to the beginning of 2002. A (t) = 699/((t+1)^0.94) \\\\\ (0<=t=5\) What was the average selling price of standalone DVD recorders at the beginning of 2003? At the beginning of 2006? Round your answers to the nearest dollar.) 2003_______ 2006 _______
- Andy buys a new car for $23,540. He estimates that the car will decrease in value by about 5% each year. Which of the following functions best models this situation?The Circle "K" Club is planning a service project for children at a local children's home. They plan to rent a "Dora the Explorer Moonwalk" for the event. The cost of the moonwalk will include a $95 delivery fee and $45 for each hour it is used. Write a function that describes the cost C for renting the moonwalk in terms of x, the number of hours used.Taxi Miles The Inner City Taxi Company estimated,on the basis of collected data, that the number of taximiles driven each day can be modeled by the function Q = 489L0.6, when they employ L drivers perday.a. Graph this function for 0 <= L <= 35.b. How many taxi miles are driven each day if thereare 32 drivers employed?c. Does this model indicate that the number of taximiles increases or decreases as the number ofdrivers increases? Is this reasonable?d. Is the graph of this function concave up or concavedown? What does this mean?