Section 4.8: Exponential Growth & Decay FINAL EXAM!!!! Tuesday May 7th Wednesday May 8th Section 4.8: Exponential Growth & Decay

Compounded Interest Review An initial deposit is made in a savings account for which the interest is compounded continuously. The balance of the account will quadruple in 80 years. When will the balance of the account reach $41,000 if the initial deposit was $8,000?

Exponential Growth and Decay The amount A of an object present at time t is given by where A0 is the original amount of the object and k is the rate of decay or growth (k > 0 if growth and k < 0 if decay) k > 0 k < 0

Bacterial Growth A colony of bacteria grows according to the law of uninhibited growth. If 100 grams of bacteria are present initially, and 250 grams are present after two hours, how many will be present after 4 hours?

Half-Life The half-life of Uranium-234 is 200,000 years. If 50 grams of Uranium-234 are present now, how much will be present in 1000 years (Half-life is the time required for half of a radioactive substance to decay).

Bacterial Growth Practice A colony of bacteria starts with 100 bacteria and increases according to the law of uninhibited growth. a) If the number of bacteria doubles in 3 hours, find the function that gives the number of cells in the culture. b) How long will it take the size of the colony to triple? c) What is the population of the bacteria after 8 hours?

Newton’s Law of Cooling u0 = Initial temperature of the heated object k = negative constant t = time u = temperature at a given time, t T = constant temperature of the surrounding area

Newton’s Law of Cooling Practice An object is heated to 100C (degrees Celsius) and is then allowed to cool in a room who’s air temperature is 30C. If the temperature of the object is 80C after 5 minutes, when will its temperature be 50C?

Section 4.8: Exponential Growth & Decay FINAL EXAM!!!! Tuesday May 7th Wednesday May 8th Homework #23: pg 334 #5, 9, 13 (a& b), 21 STUDY GUIDE!