2 A. Dr. Steve is working with a new radioactive substance in his lab. He currently has 64 grams of the substance and knows it decreases at a rate of 25% every hour. The is . The situation represents exponential . The rate, r, is . B. Dr. Steve needs to calculate how long it will take his 64-gram sample of a radioactive substance to decay to 27 grams. To write the expression to model the amount of radioactive substance remaining, substitute for A and b in the general form of an exponential expression. A = b = (to find b, substitute for r in the equation r = 1 - b and solve.) A(b)t = ( )t The value of this expression needs to equal the remaining amount, 27 grams. C. 27 = 64(0.75)t (27 64 ) = (0.75) (27 64 ) = (3 4 (3 4 ) 3= (3 4 ) ) The substance will decrease from 64 grams to 27 grams after hours. = t Guided Notes: Writing and Solving Exponential Equations Edmentum. Permission granted to copy for classroom use. 4 For problems involving interest that is not compounded annually, this formula can be used: =0(1+ n ) P0 is the is the interest rate. . is the number of times per year the interest is compounded. Example: $300 is placed in account where it earns 4% interest. How much will be in the account after 5 years if the interest is compounded annually? What if it was compounded quarterly? 4 % Compounded Annually 4 % Compounded Quarterly A(b)x = ( )5 (4)(5) P = 3