Exponential equations: Any equation with a variable used as part of an exponent.

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Victor Rose
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1 Write the 4 steps for solving Exponential equations Exponential equations: Any equation with a variable used as part of an exponent. OR 1) Make sure one and only one side of the equation is only a base raised to a variable expression. both sides are only a base(same OR base) raised to an exponent. 2) Take the logarithm (with the same base) of each side. In order to isolate a variable that is an exponent of an equation, you need to re write the equation as the equivalent equation using logarithms. 3) Apply the Power Properties of Logarithms. 4) Solve any resulting equation for the desired variable algebraically Mar 2 9:30 PM 1

2 1) Make sure one and only one side of the equation is only a base raised to a variable expression. 2) Take the logarithm (with the same base of each side. 3) Apply the Power Properties of Logarithms. 4) Solve any resulting equation algebraically Mar 2 9:31 PM 2

3 When the base is 10 use common log When the base is e use natural log When the base is any other number use log base b Mar 2 9:31 PM 3

4 1) Make sure one and only one side of the equation is only a base raised to a variable expression. 2) Take the logarithm (with the same base) of each side. 3) Apply the Power Properties of Logarithms. 4) Solve any resulting equation algebraically Mar 2 9:31 PM 4

5 1) Make sure one and only one side of the equation is only a base raised to a variable expression. 2) Take the logarithm (with the same bas of each side. 3) Apply the Power Properties of Logarithms. 4) Solve any resulting equation algebraically Mar 2 9:31 PM 5

6 Some calculators have a function for any base, but with others you will need to use the Change of Base Property. You can use the log with any base, t, in this property Mar 2 9:32 PM 6

7 Mar 2 9:32 PM 7

8 Notes 9 10 common natural need to be in exponent form before you do this Dec 30 9:10 PM 8

9 Dec 30 9:11 PM 9

10 5. You deposit some money in an account. It is left there for 25 years, without making any additional deposits or withdrawals. Determine the rate of interest, compounded continuously, required to quadruple your investment. Dec 30 9:13 PM 10

11 6. Maria invested $3000 in an individual retirement account (IRA) which earns annual interest of 4.9%. How long will it take her to have $9000 in her IRA? Dec 30 9:15 PM 11

71t, where t is the time in hours and N o is the initial

12 7. The population of a certain strain of bacteria grows according to the formula N = N o t, where t is the time in hours and N o is the initial population. How long will it take 50 bacteria to increase to 500,000? Dec 30 9:15 PM 12

13 8. 12 m + 5 = 17 Approximate log Now find it more precisely. Dec 30 9:16 PM 13

14 Jan 18 12:15 PM 14

15 Jan 18 12:16 PM 15

16 1) Make sure one and only one side of the equation is only a base raised to a variable expression. 2) Take the logarithm (with the same base) of each side. 3) Apply the Power Properties of Logarithms. 4) Solve any resulting equation algebraically Jan 18 12:15 PM 16

17 1) Make sure one and only one side of the equation is only a base raised to a variable expression. 2) Take the logarithm (with the same base) of each side. 3) Apply the Power Properties of Logarithms. 4) Solve any resulting equation algebraically Jan 18 12:16 PM 17

18 Mar 2 9:32 PM 18

8.1 Exponential Growth 1. Graph exponential growth functions. 2. Use exponential growth functions to model real life situations.

8.1 Exponential Growth 1. Graph exponential growth functions. 2. Use exponential growth functions to model real life situations. 8.1 Exponential Growth Objective 1. Graph exponential growth functions. 2. Use exponential growth functions to model real life situations. Key Terms Exponential Function Asymptote Exponential Growth Function