N 16-6 Exponential and Logarithmic Applications Growth and Decay Formulas Exponential Growth or Decay: A(t) = A0bt 1 Half-life: A t A 0 2 t k r Compound Interest: A(t) = P 1 n nt Continuously Compounded Interest: A(t) = Pert Continuous Growth or Decay: A(t) = A0ekt 1. Upon graduating from college, Ashley took a job with a starting salary of $40,000. She can expect a 6% raise in pay each year. In notes 7-6 we found by graphing that after 6.959 years Ashley would be earning $60,000/year. Confirm this result algebraically. N 16-6 2. Living organisms can be dated by the amount of carbon-14 present at time t compared to the amount present when the organism was alive. The half-life of carbon 14 is 5730 years. How long would it take for a 185 microgram sample of carbon14 to decay to 24 grams? (Round to the nearest 100 years.) 3. Suppose a culture of bacteria is put in a petri dish and grows continuously. The culture doubles every 4 hours. a) Write a function to model the continuous growth of the bacteria. b) If the initial amount of bacteria is 100, how many bacteria will there be in 15 hours? (Round to the nearest whole number.) c) When will the bacteria count be 350,000? N 16-6 4. Suppose you plan to invest $2500 at an annual rate of 7.5%. a) How much will you have in the account after five years if the balance is compounded quarterly? b) How long will it take to have $10,000 if the balance is compounded quarterly? c) How long will it take to have $10,000 if the $2500 is compounded continuously?