Chapter 3:Exponential & Logarithmic Functions

Section 3.1

100

The function denoted by f(x)=a^x

what is an exponential function/ exponential function f with base a?

200

exponential functions and logarithmic function are examples of ...

what are transcendental functions?

300

e = 2.71828...

what is the natural base?

400

f(x)=e^x

what is the natural exponential function?

500

if you let the number of compoundings n increase without bound, the process approaches ...

what is continuous compounding?

Section 3.2

100

the inverse of a one-to-one function, the function given by f(x)=log_ax

what is the logarithmic function with base a?

200

the logarithmic function with base 10

what is the common logarithmic function?

300

the inverse of the function f(x) = e^x

what is the natural logarithmic function?

400

log_aa^x=x and a^loga(x)=x

what are inverse properties?

500

if log_ax = log_ay, then x=y.

what is the one-to-one property?

Section 3.3

100

log_ax=lnx/lna

what is the change of base formula?

200

condense the following jsing properties of logarithms: log_au + log_av

what is log_a(uv)?

300

condense the following using properties of logarithms: log_au - log_av 

what is log_a(u/v)?

400

condense the following using properties of logarithms: log_auⁿ

what is nlog_au?

500

condense the following using properties of natural logarithms: lnuⁿ

what is nlnu?

Section 3.4

100

solving a logarithm by writing it in exponential form

what is exponentiating both sides of an equation?

200

lnx=3 is called 

what is logarithmic form?

300

e^lnx=e^{3 is calle...}

what is exponentiate each side?

400

x=e³

what is exponential form?

500

a^x=a^y if and only if x=y

what is one-to-one properties?

Section 3.5

100

name the mathematical model: y=ae^bx, b>0

what is the exponential growth model?

200

name the mathematical model: y=ae^-bx, b>0

what is the exponential decay model?

300

name the mathematical model: y=ae^{-(x-b)^2/c ;} is normally distributed and its graph is called a bell-shaped curve

What is the Gaussian model?

400

name the mathematical model: y=a/(1+be^-rx)

What is the logistic growth model?

500

name the mathematical model: y=a+blnx and y=a+blog₁₀x

What are the logarithmic models?