Ch. 4, 5, 14 (Exps, logs, conics)

a^x , x is a positive integer

a * a * a….(x times)

a^-x , x is a positive integer

1/a^x

a^x * a^y

a^x+y

a^x/a^y

a^x-y

(a^x)^y

a^xy

a⁰

1

a^x/y

x is the power, y is the root

radical form for a^m/n

where n is even

lxl

e = ?

e is approximately…

2.718…

f(x) = b^x, b>1

f(x) = b^x, 0<b<1

f(x) = e^x

log_a(xy)

log_a(x) + log_a(y)

log_a(x/y)

log_a(x) - log_a(y)

log_a(x^y)

y * log_a(x)

Change of base formula , log_b(a)

loga/logb = lna/lnb

ln(1)

0

ln(e)

1

f(x)=log_b(x), b>1

f(x)=log_b(x), 0<b<1

f(x)=lnx

Investment equation simple interest A=

A=P(1+rt) ; P=principle, r=interest rate (decimal), t= # of years

Investment equation compound interest A=

P=principle, r=interest rate (decimal), t= # of years

Investment equation continuous interest A=

A=P(e)^rt ; P=principle, r=interest rate(decimal), t = # of years

Population growth y =

y = B(e)^kt , k > 0

Radioactive decay y =

y = B(e)^kt, k < 0

Population growth model

Radioactive decay model

Bounded growth y =

y = A - B(e)^-kt, t => 0

Logistic growth y =

Bounded growth graph

Logistic growth graph

Standard form of a conic

Ax² + By² + Cx + Dy + E + 0 ; A & B cannot both = 0

What is the focus and directrix of a parabola? y = a(x-h)² + k

Focus→ (h, k +1/4a)

Directrix→ y = k - 1/4a

Intercept form of a circle

Intercept form of a ellipse

Intercept form of a hyperbola

In a Conic section, c = ?

The distance from the center to the focus/foci

To find the foci…

ellipse: c² = a² - b²

hyperbola: c² = a² + b²

To find the asymptotes for a hyperbola…

(y-k) = +-b/a(x-h)

Is the graph of…

Point (h,k)

Is the graph of…

empty set

Is the graph of…

Two lines (asymptotes)

Is the graph of…

A hyperbola (still)