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6.2 – Exponential Functions
Key Terms
 e – The irrational number e 2.7182818284590…
 You can approximate e by substituting large values of n into the expression
 Compound Interest – Interest applied to both the principal and any previously earned interest.
 Exponential Decay – A condition in which a quantity decreases exponentially over time.
 The quantity decreases at a rate that is proportional to the current value of the quantity.
 Exponential decay can be modeled by the equation , where = the amount at time t, = the initial amount, t = time, and k = a constant called the decay constant.
 If a quantity decays exponentially, its halflife is a constant.
 A situation in which a quantity decreases by a common ratio at regular intervals.
 Exponential Function – A function that has the form , where the coefficient a is a constant, the base b is positive but not equal to 1, and the exponent x is any number.
 Exponential Growth – A condition in which a quantity increases exponentially over time.
 The quantity increases at a rate that is proportional to the current value of the quantity.
 Exponential growth can be modeled by the equation , where = the amount at time t, = the initial amount, t = time, and k = a constant called the growth constant.
 If a quantity grows exponentially, its doubling time is a constant.
 A situation in which a quantity increases by a common ratio at regular intervals.
 HalfLife – The time it takes for a quantity to decrease to onehalf of its size or value.
 If a quantity is decaying exponentially, its halflife is a constant.
 Principal – The amount of money invested or borrowed.
Notes
Exponential Functions 
 Functions with a variable in the exponent
 Formula for Exponential Functions (General Form)
 Exponential Growth and Decay

Exponential Growth 
Exponential Decay 
 An exponential growth function represents a quantity that has a constant halving time.

 An exponential decay function represents a quantity that has a constant halving time.
 Either the exponent is negative (like ) or the base will be between 0 and 1 (like ).

 Exponential growth and decay functions are written in standard form as , where is an initial amount, b is the growth factor, k is the growth rate, and t is time.

Compounding Interest Periodically 
 Compound interest is an example of exponential growth because as more time passes, the amount of money grows faster and faster.
 Formula
 A: Amount of money accumulated in the account. Amount depends on time: A depends on t, so A(t).
t: Time that money remains invested at the given interest rate. Number of periods.
P: Principle is the original amount invested.
r: Interest Rate. Ex. 9% = 0.09. Use decimal values for calculations.
n: Number of times that interest is compounded per year.

Examples
 Ex 1. Find F(3), when
 Substitute:
 Answer:

 Ex 2. Find F(3), when
 Substitute:
 Answer:

 Ex 3. Find F(4), when
 Substitute:
 Answer:

 Ex 4. Find F(3), when
 Substitute:
 Answer:

 Ex 5. Find F(4), when
 Substitute:
 Answer:

 Ex 6. Find F(2), when
 Substitute:
 Simplify:
 Expand:
 Answer:

 Ex 7. How much would $200 invested at 6% interest compounded annually be worth after 6 years? Round your answer to the nearest cent.
 Formula:
 Substitute:
 Simplify:
 Simplify More:
 Answer: $283.70

 Ex 8. How much would $500 invested at 6% interest compounded monthly be worth after 5 years? Round your answer to the nearest cent.
 Formula:
 Substitute:
 Simplify:
 Simplify More:
 Answer: $674.43

 Ex 9. How much would $400 invested at 9% interest compounded continuously be worth after 3 years? Round your answer to the nearest cent.
 Formula:
 Substitute:
 Simplify:
 Answer: $523.99

Important!
Practice (Apex Study 6.2)
 Try practice problems on Pgs 10, 20
 Mandatory: write and answer problems on Pgs 11, 21
 2 Quizzes
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