Algebra 7.1-7.2 Exponential Functions

Exponential Function

F(X) = a x b^x

A ≠ 0, B > 0 (CANNOT BE NEGATIVE), B ≠ 1

0

In the function F(X) = a x b^x .

A Is NOT EQUAL to….

Negative, 0

In the function F(X) = a x b^x .

B CANNOT EVER be… And does not equal…

Asymptote

Lin which the graph of a function APPROACHES but NEVER TOUCHES

Y = K

H value

(X), Horizontal translation

K Value

(Y) Vertical translation,

Figures out Asymptote (WHEN y=k)

used to find the range

Exponential growth

Function approaches POS INFINITY (in terms of Y)

INCREASE

B > 1

Exponential Decay

Function approaches NEG INFINITY (in terms of Y)

DECREASE

0<B<1

EG formula

A(T) = a(1 + r)^t.

where A(t)= amount of time

R= rate of inc/dec

(value) - 100%, when solving

ED formula

A(T) = a(1 - r)^t.

where A(t)= amount of time

R= rate of inc/dec

100 % - (value), when solving

constant percentage rate

EG and ED functions both model quantities that INCREASE or DECREASE by a…

Exponential equations

An equation which can be solved ALGEBRAICALLY or by GRAPHING a system of equations.

**THE INDEPENDENT VARIABLE is an exponent

Compound Interest

Interest paid monthly, which eventually turns into interest already earned.

Compound Interest Formula

Exponential model that is used to calculate the value of an investment when interest is compounded

A= P(1 + r/n)^nt

Annually

N=1

Semi-Annually

N=2

Quarterly

N=4

Monthly

N=12

Bi-weekly

N=24

Daily

N=365

Weekly

N=52