Bellwork Evaluate each expression Solve. for x = 2 7. 250 bacteria that double 1. every 30 minutes. Find the 2. number of bacteriaafter 3 hours. 3. 4.

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Bellwork Evaluate each expression Solve. for x = bacteria that double 1. every 30 minutes. Find the 2. number of bacteriaafter 3 hours Write each multiplier. 5 14% growth 6. 23% decay

Lesson 6.2 Exponential Functions

Why? You can use exponential functions to calculate the value of investments that earn compound interest and to compare different investments by calculating effective yields.

Objectives: Classify exponential function as representing exponential growth or decay. Calculate the growth of investments under various conditions.

Notes on Lesson 6.2 Exponential Functions The functions f(x) = is an EXPONENTIAL FUNCTION with base b, where b is a positive real number other than 1 and x is any real number. Graphs of Exponential Functions ** Exponential Growth ** Exponential Decay **If b>1 then it represents exponential growth. If 0<b<1 then it represents exponential decay.

Notes: Graphing Exponential Functions The constant in front and the number ± combined is the y-intercept! EXAMPLE: 1) This represents an exponential growth (2%) and the y- intercept is 5. 2) 3)

Practice: Determine whether the exponential functions represent a growth or decay and identify the y-intercept. 1) 2) 3) 4)

Functions we have learned… Linear Functions Quadratic Functions Exponential Functions Absolute Value Functions

Identify the functions below: 1) 2) 3) 4) 5.

Compound Interest Formula: A is the compound interest earned P is the principal r is the annual interest rate n is the number of times interest is compounded per year, t is the time in years Annually = 1Quarterly = 4 Semi-annually = 2Daily = 365 Monthly = 12Weekly = 52 n could be equal to:

Compound Interest Formula: EXAMPLE: Find the final amount of a $500 investment after 8 years at 7% interest compounded quarterly. ≈ $871.11

Compound Interest Formula: Practice: Find the final amount of a $800 investment after 10 years at 5.3% interest compounded semi- annually.

Compound Interest Formula: Practice: Find the final amount of a $1,200 investment after 10 years at 7% interest compounded monthly.

Lesson 6.2 Worksheet 6.2 and 4 graphs