Chapter 3

3.1

100

What is the X-Value of the function y=2^x when y=8?

X=3

200

What is the domain and range of the function f(x)=4^x?

Domain=All Real Numbers

Range=y>0

300

Describe the transformation of the function     f(x)=3^x-2+3.

The parent function 3^x is translated two units right and three units up.

400

In the equation A=P(1+r/n)^nt, what does P stand for?

The principle amount.

500

Find the final amount of money you obtain after 5 years when the initial amount is $9000 and the amount increases at a rate of 2.5% annually.

(9000)(1+0.025/1)⁽¹⁾⁽⁵⁾= $10,182.67

3.2

100

Change 5=2^x into logarithmic form.

log₂5=x

200

Solve for log₅x=y when X=625.

y=4

300

If log_ax=log_ay, then x=y due to what property?

The One-to-One property.

400

Solve for y when the equation is log₅5⁷=y.

y=7

500

What is the natural log of 1?

It is 0.

3.3

100

The equation ln2-ln5 can also be rewritten as what?

ln(2/5)

200

The logarithm log_a(xy) can also be rewritten as what?

log_ax+log_ay

300

Expand the logarithm log₅2x²y⁵.

log₅2+2log₅x+5log₅y

400

Condense the equation 3log₂3y-5log₂7x

log₂(3y³/7x⁵)

500

Does log₁₀(1/100)=log₁₀100?

No

3.4

100

Solve x for 5(2^x)=25. You may use a calculator. Round to the nearest thousandth. 

x=2.322

200

Solve for x when log₁₃(x+5)=log₁₃(-3x+33)

x=7

300

Solve x for 3^x-2=81. 

x=6

400

log₂x+log₂(x-3)=2. Solve for x

x=4

500

12(1-4^x)=18. Solve for x.

There is no solution.

3.5

100

If the rate of an equation is negative, then the equation must be an example of what model?

Exponential Decay.

200

The equation y=ae^rt is a mathematical model for what?

Exponential growth.

300

What is the half-life of the population of roaches when the initial population is 5,686?

2843 Roaches.

400

A man invests $2000 with a 3.5% increase every year. What is the final amount of money the man gets back after 4 years?

About $2300.55.

500

A population of people has an epidemic where a disease breaks out. The initial population of 5000 people decreases at a rate of 5% per year. How many years would it take for the number of people to drop to half of its initial population? Round to the nearest year.

About 14 years.