Content Standards F.IF.7e Graph exponential and logarithmic functions, showing intercepts and end behavior, and trigonometric functions, showing period,

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Presentation transcript:

Content Standards F.IF.7e Graph exponential and logarithmic functions, showing intercepts and end behavior, and trigonometric functions, showing period, midline, and amplitude. F.LE.2 Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input- output pairs (include reading these from a table). Mathematical Practices 1 Make sense of problems and persevere in solving them.

Then/Now You evaluated numerical expressions involving exponents. Graph exponential functions. Identify data that display exponential behavior.

Vocabulary exponential function exponential growth function exponential decay function

Concept

How We Graph Exponential Functions A. Graph y = 4 x. Find the y-intercept and state the domain and range. Graph the ordered pairs and connect the points with a smooth curve. Answer: The graph crosses the y-axis at 1, so the y-intercept is 1. The domain is all real numbers and the range is all positive real numbers.

Example 1 A. Graph y = 5 x. Find the y-intercept and state the domain and range.

YOU TRY A. Graph y = 3 x. Find the y-intercept and state the domain and range.

Example 2 A. Graph Find the y-intercept and state the domain and range.

Example 3 – REAL LIFE Use Exponential Functions to Solve Problems A. DEPRECIATION Some people say that the value of a new car decreases as soon as it is driven off the dealer’s lot. The function V = 25,000 ● 0.82 t models the depreciation of the value of a new car that originally cost $25,000. V represents the value of the car and t represents the time in years from the time the car was purchased. What is the value of the car after five years?

YOU TRY A.$21,000 B.$23,600 C.$18,040 D.$20,000 B. DEPRECIATION The function V = 22,000 ● 0.82 t models the depreciation of the value of a new car that originally cost $22,000. V represents the value of the car and t represents the time in years from the time the car was purchased. What is the value of the car after one year?