Growth Factor (b) = 1 ± Growth Rate (r) Starter Thursday February 12, 2015 Give the mathematical model for the situation that has the following growth factor/growth rate and given initial amount. 1. Growth factor: 3 2. Growth rate: 9.2% Initial value: 1 2 Initial value: 2 Remember: Growth Factor (b) = 1 ± Growth Rate (r)

The answer looks like this: Logarithm Equations What is an Exponent? 2 3 What is a Logarithm? A logarithm goes the other way. It asks, “what exponent produced this?” exponent base The exponent of a number says how many times to use the number in a multiplication. 2 ? = 8 The answer looks like this: 𝐥𝐨𝐠 2 8 =3 2 3 =2∗2∗2 2 3 = 8 Exponents and Logarithms: “undo” each other (as long as they have the same base) Are inverses of each other

Logarithm Equations Rewrite each equation in exponential form: 2 3 = 8 𝐥𝐨𝐠 2 8 =3 Rewrite each equation in exponential form: Rewrite each equation in logarithmic form: log 3 x =4 log y 2 =5 log 1 y =x log 30 =x 4 3 =64 3 x =27 8 0 =1 x= y −12

Natural Logarithm Write in exponential form: 𝑒 𝑥 𝐥𝐨𝐠 𝑒 𝑥 When the base is e, we get: The Natural Logarithm 𝐥𝐨𝐠 𝑒 𝑥 Also knowns as ln(𝑥) Write in exponential form: 5. ln 𝑦=𝑥 6. ln 𝑥=15 Write in logarithmic form: 5. 𝑒 15 =𝑥 6. 𝑒 𝑛 =3

Evaluating log 3 9 log 2 16 log 4.1 log 2 32 log 2 32 = log 32 log 2 2 3 = 8 𝐥𝐨𝐠 2 8 =3 Evaluate each expression without a calculator. log 3 9 log 2 16 Evaluate each expression WITH a calculator. log 4.1 log 2 32 Enter in the calculator like this: log 2 32 = log 32 log 2 log 37