Chapter 3 Review

Exponential function behavior

100

Determine whether f(x)=7(1.2)^x represents growth or decay.

Growth, because the base 1.2 > 1

200

Identify the decay factor in g(x)=14(0.82)^x

Decay factor = 0.82

300

A population follows P(t)=1200(1.06)^t. What is the percent growth rate?

Growth rate = 6%

400

A medicine model is M(t)=480(0.65)^t. How much remains after 3 hours?

≈131.6

500

Compare A(t)=500(1.04)^t and B(t)=550(0.98)^t after 10 years.

A≈740.1

B≈450.1 → A larger.

log/exponential conversion & evaluation

100

Rewrite log₄(64)=3 in exponential form

4³=64

200

Rewrite 2⁵=32 in logarithmic form

log₂(32)=5

300

Evaluate log₃(1/27)

-3

400

Evaluate ln e^-2

-2

500

Which is larger: log₅(30) or log₅(32)?

log₅(32)

Expanding and condensing

100

Expand: log(5x)

log5 + logx

200

Expand: ln(x² / 3y)

2ln x - ln3 - ln y

300

Condense: 4log x - log 7

log(x⁴/7)

400

Condense: ln a + 1/2 ln b - ln 4

ln(ab^1/2/4)

500

Who is correct for log(x)+log(x+3)?

Student A: log(2x+3)

Student B: log(x²+3x)

Justify using log properties

Student B: log(x²+3x)

Solving Exponential equations

100

Solve: 3^x=27

x=3

200

Solve: 8^(2x-3)=1/8

x=1

300

4^(x+1)=30

x≈1.953

400

12(1.05)^t=30

t≈18.73

500

When will B(t)=240(1.11)^t reach 550?

t≈8.1

Solving Logarithmic Equations

100

log₂(x)=3

x=8

200

log(4x)=6

x=250,000

300

log(x-2)+log(3)=2

x=34

400

log₅(x)-log₅(4)=2

x=100

500

Solve: log(x+1)+log(x-4)=2 and explain why the equation only has one solution. 

x=13