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#1: The brain mass of a human fetus during the last trimester can be accurately estimated from c3 1500 the circumference of the head by m(c) = E T' where m(c) is the mass of the brain (in grams) and c is the circumference (in centimeters) of the head. (a) Estimate the brain mass of a fetus that has a head circumference of 30 cm. (b) Find the rate of change ofthe brain mass for a fetus that has a head circumference of 30 cm and interpret your results. #2: Researches have used the Richardson model to develop the following function that can be used to accurately predict the weight of Holstein cows (females) of various ages: W(t) = 619(1 0.905e'0'002t)1'2386, where W(t) is the weight of a Holstein cow (in kg) that is t days old. (a) What is the maximum weight ofthe average Holstein cow? (b) At what age does a cow reach 90% of its maximum weight? (c) Find W'(1000). #3: The metabolic rate after a person eats a meal tends to go up and then, after some time has passed, returns to a resting metabolic rate. This phenomenon is known as the thermic effect of t food and can be described for a particular individual as F(t) = 10.28 + 175.9te_, where F(t) is the thermic effect of food (in kJ/hr), and t is the number of hours that have elapsed since eating a meal. Find the time after the meal when the thermic effect of the food is maximized. #4: The percent of concentration of a certain drug in the bloodstream t hours after the drug is administered is given by [(0') = 3:4. K(1) = 3(1) 3% = 0.6% = 0.006. 12+4 _ (3) Find the time at which the concentration is a maximum. (b) Find the maximum concentration. For example, after 1 hour the concentration is given by #5: A 17ft ladder is placed against a building. The base ofthe ladder is slipping away from the building at a rate of9 ft per minute. Find the rate at which the top ofthe ladder is sliding down the building at the instant when the bottom of the ladder is 8 ft from the base of the building. {'2 #6: A population grows at a rate P'(t) = 500te_?, where P(t) is the population after t months. (a) Find a formula for the population size after t months, given that the population is 2000 at t = 0. (b) Use your answer from part a to nd the size of the population after 3 months. #7: Evaluate the denite integral. 3 l 1 foxs x3+9dx #8: The rate of reaction to a drug is given by r'(t) = the't, where t is the number of hours since the drug was administered. Find the total reaction to the drug form t = 1 to t = 6