Day 18: Exponential Functions Goal: To evaluate, identify and graph exponential functions. Standard: – Represent relationships in various contexts using equations involving exponential functions; solve these equations graphically or numerically. Know how to use calculators, graphing utilities or other technology to solve these equations. Guiding Question: How can I graph, evaluate and identify exponential functions? Materials: Pencil, Folder, Student Packet 1

Conversions: How many feet are in 1.2 miles? "When converting make sure your labels cancel” Time: "The short hand on the clock gives the hour, the long hand gives the minute" Find the perimeter: "Perimeter is the distance around an object" Reflection Starters: “I know……” or “I need to work on……” Math Review Day 18 Menta l Math 2

Access: Simplify each expression: A) 3 -2 B) 5 4 C) 2(3) 3 D) 2/3(3) 4 3

Exponential Function: A)The function f(x) = 500(1.035) x models the amount of money in a certificate of deposit after x years. How much money will there be in 6 years? B) The function f(x) = 200,000(0.98) x, where x is the time in years, models the population of a city. What will the population be in 7 years? 4

Try: The function f(x)= 1500 (0.995) x, where x is the time to years, models a prairie dog population. How many prairie dogs will there be in 8 years? 5

Tell whether each set of ordered pairs satisfies and exponential function. Explain your answer. A) {(-1, 1.5), (0, 3), (1, 6), (2, 12)} B) {(-1, -9), (1, 9), (3, 27), (5, 45)} 6

Try: Tell whether the set of ordered pairs satisfies an exponential function. Explain your answer: {(- 1, 1), (0, 0), (1, 1), (2, 4)} 7

Graph: A)y = -1/4 (2) x B)-1(1/4) x C) y = 4(0.6) x 8

Try: Graph A)y = -6 x B) y = 4(1/4) x 9

Exponential Growth: Exponential Decay: Compound Interest: 10

A)A sculpture is increasing in value at a rate of 8% per year, and its value in 2000 was $1200. Write an exponential growth function to model this situation. The find the sculpture's value in2006. B) Write a compound interest function to model the situation, then find the balance after the given number of years. $1200 invested at a rate of 3.5% compound quarterly; 4 years 11

Try: A)The original value of a painting is $9000 and the value increases by 7% each year. Write an exponential growth function to model this situation. Then find the painting's value in 15 years. B) The population of a town is decreasing at a rate of 3% per year. In 2000, there were 1700 people. Write an exponential decay function to model the situation. Then find the population in

General Forms of Functions: Linear: Quadratic: Exponential: 13

Look for a pattern in the data set to determine which model best describes the data: 14

Try:Look for a pattern in the data set to determine which model best describes the data: 15

Exit Slip (on a half-sheet of scratch paper) A)The function y = 11.6(1.009) x models residential energy consumption in quadrillion Btu where x is the number of years after What will residential energy consumption be in 2013? B) Graph y = -0.5(3) x C) What kind of model best describes the data set? 16

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