Math 141 Exam 3 Review - Winter

Exponential Function Facts

100

Domain of exponential functions:

(-∞,∞), All reals, ℝ

200

Range of exponential functions

(0,∞) {y|0<y}

300

What does y=0 represent?

Horizontal Asymptote

400

What determines exponential growth or decay in terms of the base?

Growth: 1 < b

Decay: 0 < b < 1

500

What term describes exponential functions? or What is the relationship of the inputs and outputs of an exponential function?

1:1, 1-1, one-to-one

Exponential Formulas

100

Write the definition of Exponential functions

f(x)=a^x 

200

Write the compound interest formula

A=P(1+r)^t

300

Write the continuous interest formula

A=Pe^rt

400

Write the definitions of even and odd functions;

Bonus (100 (50 each)): include graphical symmetry for each

Even: f(-x)=f(x) symmetric with respect to the y-axis

Odd: -f(-x)=f(x) symmetric with respect to the origin; point (0,0)

500

Write the three definitions of logs

log v = u exactly when v=10^u

log_b v = u exactly when v=b^u

ln v = u exactly v=e^u

Bob Loglaw's Log Blog

100

What are the standard bases of the log and ln functions?

log = base 10 and ln = base e

200

What is the product rule of logarithms?

Log_b(MN)=Log_b(M)+Log_b(N)

300

What is the quotient rule of logarithms?

Log_b(M/N)=Log_b(M)-Log_b(N)

400

What is the power rule of logarithms?

Log_b(Mk)=kLog_b(M)

500

What is the change of base formula?

Log_b(M)=Log_a(M)/Log_a(b)

Roots and Radicals

100

Simplify √243 + √48

9√3 + 4√3

200

Solve √1-2x -7=x

x=-4

300

Solve: ∛7-6x=3

x=-10/3

400

Factor: x^(2/3)-2x^(1/3)-15

(x^(1/3)-5)(x^(1/3)+3)

500

Rationalize the denominator:

f(x)=	2
	3+√6

f(x)=	6-2√6
	3

The times are changin' (at an average rate)

100

What is the average rate of change formula?

f(b)-f(a)
---------
b-a

200

Find the average rate of change: f(x)=x*2^x as x goes from 1 to 3

11

300

Find the average rate of change: f(x)=e^x-e^-x as x goes from -6 to -4

174.42

400

Find the average rate of change: f(x)=xlog(x) as x goes from 1 to 9

1.0735

500

Name two points on a graph of exponential functions (form: f(x)=a^x) used to find the model.

(0,1) and (1, a)