ObjectiveDOL  SWBAT solve and create exponential equations using logs.  (CCSS: A-CED.2)  2.4.a.ii  (CCSS: A-CED.1)  2.4.a.i  Given 2 multiple choice and 1 constructed response, students will solve and create exponential equations using logs with 80% accuracy.

 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

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

 5e -x – 7 = 2  x = -.588

AP StatsAP Calc  625e 4x = 200  x =  3e -2x + 4 = 10  x =

 A = Pe rt  Equation for cash money  P = principal  R = rate as a decimal  T = time

What is the balance after 10 years?How long will it take to make $1500?  A = Pe rt  A = 1000e (.05)(10)  A = 1000e 0.5  A = $  A = Pe rt  1500 = 1000e (.05)t  1.5 = e (.05)t  ln1.5 = ln e (.05)t  ln 1.5 =.05t  (ln 1.5)/.05 = t  t = 8.11 years

 An investment of $100 is now valued at $ The interest rate is 8% compounded continuously. About how long has the money been invested?  A = Pe rt  = 100e.08t  = e.08t  ln = ln e.08t  ln =.08t  t = 5 years At this rate, the money has been invested for approximately 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?  $  How long will it take the balance in Sarita’s account to reach $2000?  About 20.4 years