Final Exam Equations

P(1+r)^t

One-time investment & payout

P\left\lbrack\frac{\left(1+r\right)^{t}-1}{r}\right\rbrack

Annual investment & payout

x=b^y

y=log_bx

a³-b³=(a-b)(a²+ab+b²)

Difference of cubes

s(t)

Position

v(t) or s'(t)

Velocity

a(t) or s''(t)

Acceleration

a^xlna

Derivative of a^x

\frac{1}{x\left(\ln a\right)}

Derivative of log_ax

\frac{1}{x\left(\ln10\right)}

Derivative of logx/a, a<10

y-y₁=(f'(x₁))(x-x₁)

Tangent equation

P\left(1+\frac{r}{1}\right)^{1t}

Compound interest equation (annual)

P\left(1+\frac{r}{12}\right)^{12t}

Compound interest equation (monthly)

P\left(1+\frac{r}{365}\right)^{365t}

Compound interest equation (daily)

Pe^rt

Compound interest equation (continuous)

\frac{\ln2}{r}

Doubling time equation

lnA-lnB

\ln\frac{A}{B}

ax^x²(2xlna+x)

Derivative of ax^x²

x= denominator = 0

Vertical asymptote

y = the leading coefficients divided

Horizontal asymptote when numerator = denominator

y = no HA

Horizontal asymptote when numerator > denominator

y = 0

Horizontal asymptote when numerator < denominator

Slant asymptote via long division

Horizontal asymptote when numerator > denominator by 1

(Left over) numerator = 0

Finding the x-intercept

f(0)

Finding the y-intercept

\sqrt{\frac{\left(annualdemand\right)\left(reorder\cos t\right)}{\frac{\left(holding\cos t\right)}{2}}}

Inventory/order equation

\frac{x\left(D^{\prime}\left(x\right)\right)}{D\left(x\right)}

Elasticity equation

D(x)x

Total revenue equation

R’(current price)

Finding price increase value

\int a^{x}dx

\frac{1}{\ln a}a^{x}+C

\frac{\int_{x}^{x+L}f\left(x\right)}{L}

Moving average equation

\frac{1}{b-a}\int_{a}^{b}f\left(x\right)

Average value equation