Exam 2 Review for Final

Inverse Functions

100

This property determines whether a function has an inverse

A function being one-to-one ( passes the horizontal line test )

200

If f (-3) = 6, what is f^-1 (6)?

-3

300

If f(x) = 2x + 4 and g(x) = 1/2x - 2, what is their relationship

f and g are inverse functions of each other

400

For f(x) = (x+1) / (x-3), find f^-1(x)

f^-1(x) = (3x+1) / (x-1)

500

f(x) = (5x+3)/(2x-7), find f^-1(x)

f^-1(x) = (7x+3)/(2x-5)

Exponents and Logarithms

100

Express a^-n in a positive exponent form

1/aⁿ

200

Rewrite 3⁴ = 81 in logarithmic form

log₃₍₈₁₎ = 4

300

State the log property that rewrites log_a(xy)

log_a(xy) = log_ax + log_a y

400

Expand log₂(6xy) using log properties

log₂(6xy) = log₂(6) + log₂(x) + log₂(y)

500

Convert log₃(7) to base-10 logarithms 

log₃(7) = log(7) / log(3)

Solving Exponential and Log Equations

100

Solve 125^x = 5

x = 1/3

200

Solve log₂(x) = 3

x = 8

300

Solve log(x-10) - log(x-6) = log(2)

No solution

x = 2 is not allowed based on domain (x>10 and x>6)

400

Solve e^3-x = (e³)^-x

x = -3/2

500

Solve ln(7-x) + ln(1-x) = ln(25-x)

x = -2

Exponential Growth and Decay

100

For exponential growth A(t) = A₀e^kt, write the doubling time formula

T = ln2/k

200

Half-life of A(t) = 500e^-0.032t in years

t_1/2 = 21.66 years

300

If 12g decays to 6.0g in 4 years, how much is left after 7 years?

A(7) = 3.56g

400

Newton's law of cooling: A piece of metal is 300^oC and is put into a 50^oC bath; after 4 min the metal is 175^oC. Find its temperature after 12 min.

T(12) = 81.25^oC

500

For y = 246e^-8t/3, what is the slope and intercept of the line when plotting ln y vs t? 

slope = -8/3, intercept = ln(246)

Financial Math and pH

100

What is the formula for interest compounded continuously?

A = Pe^rt

200

If $5,000 is invested for 8 years at a 4% continuous interest, how much will there be in the account?

$6,885.64

300

If [H₃O⁺] = 6.3 x 10^-4, what is the pH of the solution?

pH = 3.20

400

pH = 6.5, find concentration of hydronium ions.

[H₃O⁺] = 3.16 x 10^-7

500

An investor is deciding where to deposit $10,000. Bank A 6.4% compounded annually; Bank B 6.3% compounded monthly; Bank C 6.35% compounded quarterly. Which bank will yield the highest amount of money after 5 years?

Bank B yields the highest amount of money

A: $13,640

B: $13,670

C: $13,660