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Evaluate: Write without the radical:. Objective: To graph exponential functions and inequalities To solve problems involving exponential growth and decay.

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Presentation on theme: "Evaluate: Write without the radical:. Objective: To graph exponential functions and inequalities To solve problems involving exponential growth and decay."— Presentation transcript:

1 Evaluate: Write without the radical:

2 Objective: To graph exponential functions and inequalities To solve problems involving exponential growth and decay

3 Exponential Functions have the form: A constant raised to a variable power. f(x) = b x where b >0 & b ≠ 1

4 Enter into calculator and graph: f(x) = 2 x [2nd] [table] to see list of data points Notice how quickly exponential functions grow.

5 If b u = b v then u = v When b > 0 and b≠ 1 The graph of f(x) = b x always passes through the points (0,1) and (1,b) The graph of f(x) = b x is the reflection about the y-axis of the graph of f(x)= The graph of f(x) = b x has the horizontal asymptote y = 0. There is no vertical asymptote.

6 The domain of f(x) = b x is the set of real numbers: the range is the set of positive numbers. f(x) = b x is increasing if b > 1 ; f(x) = b x is decreasing if 0< b< 1. f(x) = b x is a one-to-one function since it passes the horizontal line test.

7 f(x) = 4 x What happens to the graph f(x) =4 x +2? xy -2 1/16 ¼

8 3 10 = 3 5x 10 = 5x x = = (x-1) 7 if x > 1 2 = x-1 3 = x 3 3x = 9 x-1 3 3x = 3 2(x-1) 3x = 2x -2 x = -2

9 2 8 = 2 x+1 4 2x+1 = x+1 = 2

10 Compound Interest Exponential Growth or decay (bacteria/ radiation half life)

11 Compound interest means the each payment is calculated by including the interest previously earned on the investment.

12 Year Investment at StartInterestInvestment at End 0 (Now)$1, ($1, × 10% = ) $ $1, ($1, × 10% = ) $ $1, ($1, × 10% = ) $ $1, ($1, × 10% = ) $ $1, ($1, × 10% = ) $ $1,

13 If you have a bank account whose principal = $1000, and your bank compounds the interest twice a year at an interest rate of 5%, how much money do you have in your account at the year's end?principal interestan interest rate

14

15 . Initial Amount Final Amount Growth Rate Time

16 In t hours the number of bacteria in a culture will grow to be approximately where N 0 is the original number of bacteria. At 1 PM the culture has 50 bacteria. How many bacteria does it have at 4 PM? at noon?

17 1. If you start a bank account with $10,000 and your bank compounds the interest quarterly at an interest rate of 8%, how much money do you have at the year’s end ? (assume that you do not add or withdraw any money from the account)interest rate

18 1.

19 The average growth rate of the population of a city is 7.5% per year and is represented by the formula y=A(1.075) x, where x is the number of years and y is the most recent population of the city. The city’s population A is now 22,750 people. What is the expected population in 10 years?

20 How much money should Kelli invest now in a money market account if she wishes to have $9,000 in the account at the end of 10 years? The account provides an APR of 6% compounded quarterly.


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