Lessons 30-33 Test Review

30

100

Exponential Equation: f(x) = b^x

What does the "b" stand for?

What does the "x" represent?

b = base

x = exponent

200

f(x) = (7/9)^x - 4

Does this function represent growth or decay?

Decay

300

f(x) = 4^x - 1

Complete a table of of points for a graph where x = -2, -1, 0, 1, 2    

(-2, -15/16), (-1, -3/4), (0, 0), (1, 3), (2, 15)

400

f(x) = -(2)^{(x + 2)} - 5

Name all transformations of this function.

Reflection over x-axis, left 2, down 5

500

1/81 = 9^-3x

Solve for x

x = 2/3

31

100

A = P(1 + r)^t

P = 

r = 

t =

P = Initial amount

r = rate

t = time

200

A population of 12 million will double in 35 years. What will the population be 20 years from now?

P = P₀(2^t/d)

In this scenario, what is P₀, t, d

P₀ = 12 million

t = 20

d = 35

300

You are going to invest $2000. You plan to leave the money in the account for the next 10 years.  Calculate the account's outcome if it earns 3% interest compounded monthly.

$2698.71

400

Aluminum-26 has a half life of 740,000 years.  In 2012, a recycle center had 235,000 pounds of aluminum.  How much aluminum would we expect to be remaining in 2092?

234,982.391 pounds of aluminum

500

You are going to invest $2200 but need to decide what investment to put it in.  You plan to leave the money in the account for the next 5 years.  Calculate each account's outcome and determine which account you would invest your money in. 

Earns 2% interest compounded semi-annually

Earns 1.8% interest compounded continuously

2% compounded semi-annually = $2430.17

1.8% compounded continuously = $2407.18

First option is better.

32

100

Rewrite log₃81 = 4 as an exponential equation.

3⁴ = 81

200

Using the change of base formula, rewrite log₁₂29

log29/log12

or

ln29/ln12

300

State the domain, range, and asymptote for f(x) = log₄(x - 2)

Domain = (2, + infinity)

Range = (- infinity, + infinity)

Asymptote: x = 2

400

Condense: 2log₄x + log₄y

log₄(x²y)

500

Expand: log₂(z⁶/x⁴y³)

6log₂z - 4log₂x - 3log₂y

33

100

Solve. 3^{x + 1} = 13

x = 1.3347

200

Solve. ln(5x - 4) = 9

x = 1621.4168

300

Solve. 5(2^x) + 7 = 11

x = -0.3219

400

Solve. log(x - 1) + log(x) = log(2)

x = 2

500

Solve. e^2x - 4e^x - 5 = 0

x = 1.61