Algebra 2 Chapter 10 Review

Natural Logarithms

100

Evaluate: - ln 1

0

200

Evaluate: ln 1/(³√(e^2))

-2/3

300

Solve: ln x + ln 3 = ln (x+4)

x = 2

400

Solve: 3e^2x + 2 = 50

x = ln 4

500

3e^2x -12e^x+ 12 = 0

x = ln 2

Word Problems

100

One isotope of chromium has a half-life of 23 hours. How long does it take 50 g to decay to 40 g?

7.4 hours

200

How much will a $4000 investment be worth after 5 years if it is invested at 8% interest compounded quarterly?

$5943.79

300

How long does it take an investment to double in value if it is invested at 12 % compounded monthly? 

5 years 10 months

400

The population of a certain type of bacteria doubles every 10 hours. How long will it take the population to triple?

15.8 hours

500

A colony of bacteria has 6.5 x 10⁶ members at 8AM and 9.75 x 10⁶ members at 10:30AM. Find its population at noon.

1.24 x 10⁷ members

Logarithms

100

Evaluate log₂8√(2)

 7/2

200

Solve: log₈x = -1/3

1/2

300

Express in terms of log₄A and log₄B: log₄(A²/√(B))

2 log₄A - 1/2 log₄B

400

Solve: log_ax + log_a(2x+3) = log_a2

1/2

500

log₃(x+2) + log₃6 = 3

5/2

Exponents

100

Solve: (y+1)^2/3 = 9

26

200

Simplify: 8^√(2) / 2^√(8)

2^√(2)

300

Solve: 27^x+1 = 81

1/3

400

Solve: (1/10)^y = 100^y+3

-2

500

Solve: 5^x - 6^x =0

0

Inverses/Composition

100

If f(x) = x² and g(x) = 1-2x find: g(f(x))

1-2x²

200

If f(x) = x² and g(x) = 1-2x find: f(g(x))

(1-2x)²

300

If g(x) = 1-2x find g^-1(x)

g^-1(x) = (1-x)/2

400

Determine if h(x) = x⁴-1 has an inverse and find the inverse if it exists.

No inverse, it doesn't pass the horizontal line test. 

500

Let f(x) = mx + b. For what values of m and b will f(x) = f^-1(x)?

m = 1, b = 0