Find the linear approximation L(x) of the function f(x) = √√√1 − x at a = 0. L(x) = Use L(x) to approximate the numbers 10.9 and 0.99. (Round your answers to four decimal places.) 0.9≈ 0.99≈

When a certain drug is taken orally, the concentration of the drug in the patient's bloodstream After t minutes is given by C(t)=0.06t0.0002t2 where 0t240 and concentration is measured in mg/L .When is the maximum serum concentration reached, and what is that maximum concentration?

Near the surface of the moon, the distance that an object falls is a function of time. It is given by d(t)=2.6667t2 , where t is in seconds and d(t) is in feet. If an object is dropped from a certain height, find the average velocity of die object from t=1tot=2 .

The half-life of plutonium-244 is 80,000,000 years. Find function gives the amount of carbon-14 remaining as a function of time, measured in years.

Use your schools library, the Internet, or some other reference source to find real-life applications of approximations of functions.

The population P (in millions) of Texas from 2001 through 2014 can be approximated by the model P=20.913e0.0184t, where t represents the year, with t=1 corresponding to 2001. According to this model, when will the population reach 32 million?

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).

The number of bacteria in a refrigerated food product is given by N(T)=23T256T+1,3T33 ,where T is the temperature of the food. When the food is removed from the refrigerator, the temperature is given by T(t)=5t+1.5 , where t is the time in hours. a. Find the composite function N(T(t)) . b. Find the time (round to two decimal places) when the bacteria count reaches 6,752.

A driver of a car stopped at a gas station to fill up his gas tank. He looked at his watch, and the time read exactly 3:40 p.m. At this time, he started pumping gas into the tank. At exactly 3:44, the tank was full and he noticed that he had pumped 10.7 gallons. What is the average rate of flow of the gasoline into the gas tank?

Use the result from the previous exercise to graph the logistic model P(t)=201+4e0.5t along with its inverse on the same axis. What are the intercepts and asymptotes of each function?