Calc for Business 4.1-4.3 formulas

what is the base of exponential functions?

a>0

FV=

P(1+r/m)^mt

PV=

P/(1+r/m)^mt

FV compounded continuously=

Pe^rt

PV compounded continuously=

Pe^-rt

loga(x)=y

a^y=x

Population=

P0e^rt

lne1=0

e^0=1

lne=1

e^1=e

lne^x=x

e^x=x

e^lnx=x

x>0

ln(M*N)=

lnM+lnN

ln(M/N)=

lnM-lnN

ln(M^P)=

PlnM

find t for doubled in value

2=(1+r/m)^mt

d/dxlnx=

1/x

d/dxlnf(x)=

f’(x)/f(x)

d/dxe^x=

e^x

d/dxe^f(x)=

e^f(x)*f’(x)