Chapter 4 Flashcards
Exponential Function
f(x) = bˣ
Power Function
g(x) = x³
Compound Interest
A(t) = P(1+r/n)ⁿᵗ
A(t)
Amount after t years
P
Principal
APY (Annual Percentage Yield)
(1+r/n)ⁿ
Continuous Compound Interest
A(t) = Peʳᵗ
Log Function
log(x) = (10ˡᵒᵍ⁽ˣ⁾)
Natural Log Function
ln(x) = logₑˣ(x)
No Subscript?
Take 10 To Each Side
Undefined
ln ≤ 0
Log Law 1
log(AB) = logA + logB
Log Law 2
log(A/B) = logA - logB
Log Law 3
logAᶜ = C(log)A
Special Product 1
(A+B)² = A²+2AB+B²
Special Product 2
(A-B)² = A²-2AB+B²
Special Product 3
(A-B)(A+B)=A²-B²
Initial Amount + Doubling Time
n(t) = n₀(2ᵗ/ᵈ)
Common Mistake 1
log(A+B) = logA + logB
Common Mistake 2
log(A-B) = logA - logB
Common Mistake 3
log(A/B) = logA/logB
Common Mistake 4
log¹⁰/log² = log⁵
Common Mistake 5
ln(x)⁷ = 7(ln)x
Non-Linear Equalities (Sign Chart) Step 1
Get 0 on one side.
Non-Linear Equalities (Sign Chart) Step 2
Factor other side.
Non-Linear Equalities (Sign Chart) Step 3
Find where top or bottom is equal to 0 and break x-axis at this point.
Non-Linear Equalities (Sign Chart) Step 4
Sample the signs of the factors in each interval.
Non-Linear Equalities (Sign Chart) Step 5
Tally the signs.
Non-Linear Equalities (Sign Chart) Step 6
Give the interval.
