Exponential Functions and Growth/Decay - Understanding and Applying

1. Do Now 1/22/19 • Take out HW from last week. • Text p. 310, #6-34 evens • Copy HW in your planner. • Text p. 319, #6-38 evens, 44-60 multiples of 4, & 63a • Quiz sections 6.1-6.4 Thursday

2. HomeworkText p. 310, #6-34 evens

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7. Learning Target • Learning Goal • SWBAT simplify, graph, and solve exponential expressions, equations, functions and sequences. SWBAT identify and evaluate exponential growth and decay functions

8. Section 6.3 “Exponential Functions” EXPONENTIAL FUNCTION- -a nonlinear function of the form where a ≠ 0, b ≠ 1, and b > 0. y = abx As the independent variable ‘X’ changes by a constant amount, the dependent variable ‘Y’ is multiplied by a constant factor, which means consecutive Y values form a constant ratio.

9. Section 6.4 “Exponential Growth and Decay” EXPONENTIAL GROWTH- -occurs when a quantity increases by the same factor over equal intervals of time. a > 0 and r > 0 rate of growth (in decimal form) final amount y = a(1 + r)t time initial amount growth factor

10. EXPONENTIAL DECAY- -occurs when a quantity decreases by the same factor over equal intervals of time. a > 0 and 0 < r < 1 rate of decay (in decimal form) final amount y = a(1 – r)t time initial amount decay factor

11. Using Exponential Functions Write a function representing the situation. Your salary of 20,000 increases by 4% a year. A population of 210,000 decreases by 14.5% a year. Exponential decay because the population is decreasing. Exponential growth because your salary is increasing.

12. Does the table represent exponential growth, exponential decay, or neither? Eeee exponential growth; As x increases by 1, y is multiplied by 3. Eeee

13. Interpreting Exponential Functions Determine whether each function represents exponential growth or decay. Identify the rate of change. Exponential growth because b is greater than 1. Exponential decay because b is less than 1. To determine the percent rate of change use the growth factor (1 + r ) to find the rate of growth. To determine the percent rate of change use the decay factor (1 - r ) to find the rate of decay. Growth factor: 1 + r = 1.07 Decay factor: 1 - r = 0.88 r = 0.07 r = 0.12 Rate of change = 7% Rate of change = 12%

14. On Your Own Determine whether each function represents exponential growth or decay. Identify the rate of change. Eeee Eeee

15. Rewriting Exponential Functions Rewrite each function to determine if it represents exponential growth or decay. Rewrite function so t is isolated. Rewrite function so t is isolated. Evaluate the power. Evaluate the power. Exponential decay because b is less than 1. Exponential growth because b is greater than 1.

16. On Your Own Rewrite each function to determine if it represents exponential growth or decay. Eeee Eeee

17. the interest earned on the principal and on previously earned interest. COMPOUND INTEREST P = Principal (initial investment) r = annual interest rate (as a decimal) t = time in years n = number of times interest is compounded per year

18. Compound Interest Write a function that represents the balance after t years. $2,000 deposit that earns 5% annual interest compounded quarterly.

19. Compound Interest Write a function that represents the balance after t years. $15,000 deposit that earns 10% annual interest compounded monthly.

20. Homework • Text p. 319, #6-38evens, 44-60 multiples of 4, & 63a

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