1. Aim # 7.4: How do we solve exponential equations?

2. Part 1: Solving exponential equations using “like bases”  One way to solve exponential equations is to use “like bases” because when we have like bases, then  So, the steps are:  rewrite as like bases  Set _______________________________________ equal to each other  Solve for the variable.  Ex. A : 9 2x = 27 x – 1

3. More Practice  100 7x + 1 = 1000 3x – 2  81 3 –x = 5x-6

4. Part 2: Solving exponential functions that can’t have “like bases”  What option do we have if they can’t be rewritten using like bases?  Well, we have to use our knowledge of inverse properties to solve the equations.  Steps: 1 st : Use SADMEP to get the base by itself on one side of the equal sign  2 nd : Depending on the base, add a log or natural log to the problem.  **REMEMBER – whatever you do or add to one side, you have to do or add to the other!!!!  3 rd : Use log properties and SADMEP again (if necessary) to solve for the variable.

5. EXAMPLES:  a. 4 x = 11 b. 7 9x = 15 c. 4 e -0.3x – 7 = 13

6. Interest and Depreciation

7.  If we compound:we calculate interest (per year):  Quarterly4 times  Monthly12 times  Bi-monthly24 times  Weekly 52 times  Daily365 times  EX: You deposit $4000 in an account that pays 2.92% annual interest. Find the balance after 1 year if the interest is compounded a) quarterly, b) daily, C) How long will it take to earn $8350?

8. Depreciation: The equation for depreciation is: y = a(1 – r) n So, let’s use it. EX: A new snowmobile costs $4200. The value of the snowmobile decreases by 10% each year. Find the value of the snowmobile after: a) 1 year, b) 4 years, c) How many years will it take for the value to be $800?

9. EX: You invest $500 in the stock of a company. The value of the stock decreases 2% each year. Find the value of the stock after a) 1 year, b) 3 years, c) How long will it take for the value to reach $175? More Practice:

10. Summary: Answer in complete sentences. 1. What is the difference between interest and depreciation? 2. Which formula do you use to solve interest and depreciation? 3. What are some key words in the word problem that clue you in on an interest problem? B. depreciation problem?