E XPONENTIAL W ORD P ROBLEMS Unit 3 Day 5

D O -N OW

C OMPOUND I NTEREST 1. $1500 is invested at rate of 10% per year, compounded quarterly. a) P = b) r = c) n = d) What is the balance after 9 years?

R EVIEW C OMPOUND I NTEREST 2. Suppose you invest $2350 in an account with an annual interest rate of 4%, compounded semiannually. How much will be in the account in three years?

C OMPOUND I NTEREST 3. Suppose your bank offers 3.2% interest rate, compounded monthly a) How much money should you deposit if you want to have $4500 after one year? a) How much would you have to deposit if the interest rate were 4.5% instead?

H ALF L IFE The ___________________ of a radioactive isotope describes the amount of time that it takes for ________ of the isotope in a sample to decay (become lead). This process can be modeled by the exponential function... t = time elapsed A = amount left A 0 = initial quantity of substance k = half-life of the substance

H ALF L IFE 1. The half-life of radioactive radon is 3.5 days. If we start with 200 grams, how much of it will be left after 6 days? a) Write the exponential decay function for a 200-gram sample. A 0 = _________ k = __________ b) Find the amount remaining after 6 days.

H ALF L IFE 2. The half-life of I-123, an isotope of Iodine, is 13.2 hours. a) Write the exponential decay function for a 45- mg sample. A 0 = _________ k = __________ b) Find the amount remaining after 5 hours.

H ALF L IFE 3. Magnesium-27 has a half-life of 9.45 minutes. a) Write the exponential decay function for a 10- mg sample. A 0 = _________ k = __________ b) Find the amount remaining after 15 minutes.

C LOSURE : What aspect of the half life formula makes it model decay instead of growth?