Warm Up – 4/23 - Thursday Erin deposits $1200 into a bank account that grows at an interest rate of 5%. Find the amount in the account after 3 years if the interest is compounded: A) Annually B) Monthly C) Continuously 2. Bill has had his money in a savings account for 10 years. The account currently has $2,696.70. If the account accumulates interest at a rate of 3% compounded quarterly, find how much Bill initially deposited.

Quiz Friday Sketching Exponential Functions Compound Interest/Compounding Continuously Converting an Exponential to a Log Converting a Log to an exponential

Properties of Logs CW

Rules of Logarithms log 𝑎 𝑏 + log 𝑎 𝑐 = log 𝑎 (𝑏∙𝑐) THESE RULES ONLY APPLY IF THE BASE IS THE SAME!!! log 𝑎 𝑏 + log 𝑎 𝑐 = log 𝑎 (𝑏∙𝑐) log 𝑎 𝑏 − log 𝑎 𝑐 = log 𝑎 𝑏 𝑐 log 𝑎 𝑏 𝑐 =𝑐∙ log 𝑎 𝑏

Example #1 log 3 5 + log 3 4

Example #1 - Solution When I add logs with the same base, I can multiply their insides. log 3 5 + log 3 4 = log 3 5∙4 = log 3 (20)

Example #2 log 7 4 + log 7 2 + log 7 5

Example #2 - Solution log 7 4 + log 7 2 + log 7 5

Example #3 log 8 9 − log 8 4

Example #3 - Solution When we subtract logs, we divide the insides. log 8 9 − log 8 4 log 8 9 4 , If possible reduce the fraction, if not leave it as is.

Example #4 log 7 − log 5 + log 2

Example #4 - Solution Whenever mixing addition and subtraction, work from left to right. log 7 − log 5 + log 2 log 7 5 + log 2 log 7 5 ∙2 = log 14 5

Example #5 2log 9 7

Example #5 - Solution When we multiply on the outside of the log we can move that number into the exponent on the inside! 2 log 9 7 = log 9 7 2 = log 9 49

Example #6 3 log 3 3 −2 log 3 (2)

Example #6 - Solution We ALWAYS take care of the exponents first! 3 log 3 3 −2 log 3 (2) log 3 3 3 − log 3 2 2 log 3 27 − log 3 4 log 3 27 4