SWBAT solve and create exponential equations using logs

� SWBAT solve and create exponential equations using logs. � (CCSS: A-CED. 2) � 2. 4. a. ii � (CCSS: A-CED. 1) � 2. 4. a. i Objective � Given 2 multiple choice and 1 constructed response, students will solve and create exponential equations using logs with 80% accuracy. DOL

� Essential Question: How can I solve equations when x is in the exponent?

� Note: If there is not a number with the log, assume that it is base 10

� Solve: 3 x = 11 � Hint: Should get a decimal � Round to the thousandth � Answer: 2. 564

� Solve 9 x = 45 � Hint: Should be a decimal � Round to the thousandth �x = 1. 733

� Solve 3 on your future AP exam � Solve 5 on your future AP exam

� 625 e 4 x �x = 200 = -0. 3466 � 3 e-2 x �x AP Stats + 4 = 10 = -0. 2849 AP Calc

�A = Pert � Equation for cash money � P = principal � R = rate as a decimal � T = time

�A �A = Pert 1000 e(. 05)(10) 1000 e 0. 5 $1648. 72 What is the balance after 10 years? = Pert � 1500 = 1000 e(. 05)t � 1. 5 = e(. 05)t � ln 1. 5 = ln e(. 05)t � ln 1. 5 =. 05 t � (ln 1. 5)/. 05 = t � t = 8. 11 years How long will it take to make $1500?

� An investment of $100 is now valued at $149. 18. The interest rate is 8% compounded continuously. About how long has the money been invested? � A = Pert � 149. 18 = 100 e. 08 t At this rate, the money has � 1. 4918 = e. 08 t been invested for � ln 1. 4918 = ln e. 08 t approximately 5 years. � ln 1. 4918 =. 08 t � t = 5 years

� Essential Question: How can I solve equations when x is in the exponent? � Use: log, base, investing

� If Sarita deposits $1000 in an account paying 3. 4% annual interest compounded continuously, what is the balance in the account after 5 years? � How long will it take the balance in Sarita’s account to reach $2000?

� If Sarita deposits $1000 in an account paying 3. 4% annual interest compounded continuously, what is the balance in the account after 5 years? � $1185. 30 � How long will it take the balance in Sarita’s account to reach $2000? � About 20. 4 years