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- A forest fire leaves behind an area of grass burned in an expanding circular pattern. If the radius of the circle of burning grass is increasing with time according to the formula r(t)=2t+1 , express the area burned as a function of time, t (minutes).Find the point P on the graph of the function y=√x closest to the point (5,0) The x coordinate of P is?Start with the graph of y = ln x. Find an equation of the graph thatresults from vertical stretching by a factor of 2.
- Start with the graph of y = ln x. Find an equation of the graph thatresults from horizontal stretching by a factor of 3.When a species of pigs is introduced onto an island, its population increases 15% each year. This population t years after introduction is given by P = k * a^t where k and a are constants and t is greater than or equal to 0 what is the value of a? use the graph below to help solveMedical research indicates that the risk of having a car accident increasesexponentially as the concentration of alcohol in the blood increases. The risk is modeled by R = 6e12.77x, where x is the blood alcohol concentration and R, given as a percent, is the risk of having a car accident. What blood alcohol concentration corresponds to a 17% risk of a car accident? How is this shown on the graph of R in the herewith given Figure?
- An exponential fuction is given by the equation y=3^× Using the points x and x+1 show that the y - values increase by a factor of 3 between any two points separated by x2-×1=1.In the feasibility test, the flight movement of a drone is known to have a position function height h (t) = t2 - t - 2, where t is in minutes and height h is in meters. Determine the average speed of the drone increments at intervals of 3 minutes to 6 minutes and then determine the instantaneous velocity exactly equal to the average velocity.The wolf population on Isle Royale, t years after 16 wolves are introduced, is modelled by the function: P=16e.03t How many wolves can we expect to be there after 15 years?
- Find the slope of f(x)=ln(7x) at (6,3.74). Use a graphing utility and round to the nearest hundredth.For some positive constant , a patient's temperature change, T , due to a dose, D , of a drug is given by T = (C/2-D/3)D^2 What dosage maximizes the temperature change? The sensitivity of the body to the drug is defined as . What dosage maximizes sensitivity?Given the graph of the derivative f'(x) shown below, exactly how many local maxima does f(x) have? a. 3 b. 1 c. 4 d. 7