In a hospital, a drug is given to a patient. Let f(t) be the amount of drug (in mg) in the patient's body t minutes after it is administered. The nurses want to predict how the body will absorb the drug (the shape of the graph y = f(t)) to be able to prepare the next course of action. One of them remembers about Taylor polynomials from their Calculus course and explains that they allow to predict the shape of a function by making very accurate measurements of the function at one point. They decide to do this and they find the following details about the patient's absorption of the drug: • f(15) = 140 • f'(15) = • f" (15) = 1000 _17 10 12 Use these details to approximate the average amount of drug in the patient's body over the first 2 hours: 120 1 120

Strontium 90 (Sr-90), a radioactive isotope of strontium, is present in the fallout resulting from nuclear explosions. It is especially hazardous to animal life, including humans, because, upon ingestion of contaminated food, it is absorbed into the bone structure. Its half-life is 27 years. Find the function Q(t)that expresses the amount of Sr-90 present at time t, where Q0is the amount present initially and t is measured in years.   Q(t) =        If the amount of Sr-90 in a certain area is found to be 16 times the "safe" level, find how much time (in years) must elapse before the safe level is reached.         Olivia plans to secure a 5-year balloon mortgage of $250,000 toward the purchase of a condominium. Her monthly payment for the 5 years is calculated on the basis of a 30-year conventional mortgage at the rate of 5%/year compounded monthly. At the end of the 5 years, Olivia is required to pay the balance owed (the "balloon" payment). What will be her monthly payment for…

A bacteria culture initially contains 1000 bacteria and is growing at the rate of N' (t) = 2tt-2/3 bacteria per hour. Find the function N(t) that describes the number of bacteria in the culture after t hours and use it to determine how many bacteria there are after 27 hours. Type your answer in the space below. After 27 hours, there will be bacteria in the culture.

A botanist in the field needs a quick estimate of the growth of jumping cholla cactus. In his study area, he has controlled the water and nutrients the jumping cholla receive so he can isolate the effect of sunlight on growth. He lets a function s(t) represent the average hours of sunlight per day in month t (where t= 1 is January). He lets a function g(s) represent the monthly growth of jumping cholla in centimeters at different sunlight exposures. From past experience, he quickly jots down the table below.