PreCalculus 12
5.3 Solving Exponential Equations
An exponential equation is one that has ________________ as exponents and ___________________ as bases.
We can solve simple ones by equating the ____________ and therefore also equating the ________________.
Example:
solve
42x = 8x+1
When would the exponents not have to be equal?
This is why we won’t use bases that are ________________________________________.
Example: Rewrite each as a power of 3:
1
a) 27
b) 27 3
On your Own
a) 92
b) (273)32
1
2
( )
3
81
PreCalculus 12
So when we are solving equations with different bases, we need to try and ______________ them so that both
bases are the ________________
Example: Solve each equation:
a) 4x+2 = 64x
b) 42x = 82x-3
It may be beneficial to recognize the powers of . . .
2
3
5
6
...
Alternatively, we can solve exponential equations on our graphing calculators:
i.e. 15 = 3%
Yesterday, we worked with problems involving Exponential _______________ or _______________. These
problems may be modeled by an exponential equation of the form:
& = &' 1 + )
*
+ =
+- =
. =
/ =
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PreCalculus 12
Compound Interest:
With ________________ interest, the principal of A0 dollars is invested at an annual interest rate 0. This interest
is then added back into your principal (known as _____________________) after a given amount of time
(known as a __________________ ___________________). We can create an exponential equation to solve for
the amount of money available after t years.
If a principal of A0 is invested at an annual interest rate of I, with n compounding periods per year,
the amount, A, dollars will be available after t years:
2 5*
& = &' 11 + 4
3
Example: Last summer, Katie got a job working on the oil patch and managed to save $10 000. She decided to
invest it in a college fund for the next 10 years while she goes and travels (so she could go and get a math
degree afterwards).
Find out how much she will have if it grows at:
a) 6%/annum
b) 6%/annum compounded monthly
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PreCalculus 12
On your Own:
In his spare time, Wyatt plays in a punk-rock group called The Denominators. When their band grows, Wyatt
will need to get a new guitar and amp so he decides to put his earnings from his last gig into a savings account
in hopes that it will grow. Wyatt has $1000 to deposit and needs to decide between two bank accounts.
a) Account A has an interest rate of 7%/annum and it compounds annually. How much money will Wyatt
have after 20 years with account A?
b) Account B has an interest rate of 5%/annum and it compounds monthly. How much money will Wyatt
have after 20 years with account B?
c) Which account should Wyatt put his money into?
Assignment: P. 363 # 3-6 (a,c), 7(a,b), 9(a,b), 10(a,c,e), 12, 13
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