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

2. Homework Text p. 310, #6-34 evens

3. Homework Text p. 310, #6-34 evens

4. Homework Text p. 310, #6-34 evens

5. Homework Text p. 310, #6-34 evens

6. Homework Text p. 310, #6-34 evens

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

8. Section 6.3 “Exponential Functions”
-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”
-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. y = a(1 – r)t 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. exponential growth; As x increases by 1, y is multiplied by 3.
Does the table represent exponential growth, exponential decay, or neither?
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exponential growth; As x increases by 1, y is multiplied by 3.
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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: r = 1.07
Decay factor: 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.
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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.
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17. COMPOUND INTEREST
the interest earned on the principal and on previously earned 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. $2,000 deposit that earns 5% annual interest compounded quarterly.
Compound Interest
Write a function that represents the balance after t years.
$2,000 deposit that earns 5% annual interest compounded quarterly.

19. $15,000 deposit that earns 10% annual interest compounded monthly.
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, multiples of 4, & 63a

21. Homework Practice worksheet 6.3

22. Homework Practice worksheet 6.3

23. Homework Practice worksheet 6.3
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24. Homework Practice worksheet 6.3

25. Homework Practice worksheet 6.3