The function given by A(t)=0.0295t3−0.461t2+1.739t+5.73​, 0≤t≤10​, can be used to estimate the​ amount, in billions of​ dollars, invested by large oil companies in exploration for new reserves t years after 1995. Find the relative extreme​ points, and sketch a graph of the function.

Highway engineers use f(x) = (0.905)* to estimate the likelihood, or probability, that no vehicle will enter a particular intersection within an interval of x seconds. Construct a table of f(x) = (0.905)* starting at x = 0 and incrementing by 10, until x = 50. a. Evaluate f(1) and interpret the result. b. For a time interval of what length is there only a 2% chance that no cars will enter the intersection?

According to a study, the probability that a smoker will quit smoking increases with the smoker's educational level. The probability (expressed as a percent) that a smoker with x years of education will quit is approximated by the equation f(x) = 0.831x² 18.1x + 137.3 (for 10 ≤ x ≤ 16).t (a) Find f(12). (Round your answer to three decimal places.) f(12) = 39.764 ✓ Interpret this number. [Hint: x = 12 corresponds to a high school graduate.] A smoker who is a high school graduate has a X % chance of quitting. Find f'(12). (Round your answer to three decimal places.) f'(12) = 1.844 ✓ Interpret this number. [Hint: x = 12 corresponds to a high school graduate.] When a smoker has a high school diploma, the chance of quitting is increasing ✓ (b) Find f(16). (Round your answer to three decimal places.) f(16) = Interpret this number. [Hint: x = 16 corresponds to a college graduate.] A smoker who is a college graduate has a Find f'(16). (Round your answer to three decimal places.) f'(16) = %…

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Doardcdn.com/blackboard.learn.xythos.prod/57fced8e8d3c5/61730103?X-Blackboard 3 / 5 1 100% + | 7. Decide if the following functions are one-to-one. Prove your answers. (a) f(x) = x³ - 1 (b) g(x) = 2x+4 8. Decide if the following functions are onto. Prove your answers. (a) f(x)=r³-1 (b) g(x) = 2x+4 W Y 25°F Mostly clo

The population of a town can be modelled by the function P(t)= 20 (4t+3)/(2t+5), where P is the population, in thousands, and t is the time, in years, after the year 2000 (t > 0).      Clearly label all cases (a, b, c,…). Answers must be clear to read and show all steps. Use appropriate units for your answers. What is the difference between an average rate of change and an instantaneous rate of change?