Warm-Up Exercises

Evaluate the expression without using a calculator.

ANSWER –1

ANSWER 27

1. 13

–3

2. – 25

0

Warm-Up Exercises

Evaluate the expression without using a calculator.

ANSWER 10

4. A savings account pays 3% interest compounded monthly. What is the growth factor for this account?

ANSWER 1.0075

3. 4 + 123

–2

Warm-Up ExercisesEXAMPLE 1 Graph y = b for 0 < b < 1x

Graph y = 12

x

SOLUTIONSTEP 1 Make a table of values

STEP 2 Plot the points from the table.STEP 3 Draw, from right to left, a smooth curve that

begins just above the x-axis, passes through the plotted points, and moves up to the left.

Warm-Up ExercisesEXAMPLE 2 Graph y = ab for 0 < b < 1x

Graph the function.

a. Graph y = 2 14

x

SOLUTION

Plot (0, 2) and .Then,

from right to left, draw a curve that begins just above the x-axis, passes through the two points, and moves up to the left.

1, 12

a.

Warm-Up ExercisesEXAMPLE 2 Graph y = ab for 0 < b < 1x

b. Graph y = –3 25

xGraph the function.

SOLUTION

Plot (0, –3) and .

Then,from right to left, draw a curve that begins just below the x-axis, passes through the two points,and moves down to the left.

b. 1, – 65

Warm-Up ExercisesYOU TRY for Examples 1 and 2

Graph the function.23

x1. y =

Warm-Up ExercisesYOU TRY for Examples 1 and 2

Graph the function.

2. y = –2 34

x

Warm-Up ExercisesEXAMPLE 3 Graph y = ab + k for 0 < b < 1x – h

Graph y = 3 –2. State the domain and range.

12

x+1

SOLUTION

Begin by sketching the graph

of y = , which passes

through (0, 3) and . Then

translate the graph left 1 unit and down 2 units .Notice that the translated graph passes through (– 1, 1) and

3 12

x

32

1,

– 1 2

0,

Warm-Up ExercisesEXAMPLE 3 Graph y = ab + k for 0 < b < 1x – h

The graph’s asymptote is the line y = –2. The domain is all real numbers, and the range is y > –2.

Warm-Up ExercisesEXAMPLE 4 Solve a multi-step problem

• Write an exponential decay model giving the snowmobile’s value y (in dollars) after t years. Estimate the value after 3 years.

• Graph the model.• Use the graph to

estimate when the value of the snowmobile will be $2500.

A new snowmobile costs $4200. The value of the snowmobile decreases by 10% each year.Snowmobiles

Warm-Up ExercisesEXAMPLE 4 Solve a multi-step problem

The initial amount is a = 4200 and the percent decrease is r = 0.10. So, the exponential decay model is:

Write exponential decay model.

Substitute 4200 for a and 0.10 for r.

Simplify.

y = a(1 – r) t

= 4200(1 – 0.10)t

= 4200(0.90)t

When t = 3, the snowmobile’s value is y = 4200(0.90)3 = $3061.80.

SOLUTION

STEP 1

Warm-Up ExercisesEXAMPLE 4 Solve a multi-step problem

The graph passes through the points (0, 4200) and (1, 3780).It has the t-axis as an asymptote. Plot a few other points. Then draw a smooth curve through the points.

Using the graph, you can estimate that the value of the snowmobile will be $2500 after about 5 years.

STEP 2

STEP 3

Warm-Up ExercisesYOU TRY for Examples 3 and 4

Graph the function. State the domain and range.

3. y = +114

x–1

Warm-Up ExercisesGUIDED PRACTICE for Examples 3 and 4

Graph the function. State the domain and range.

4. y = 5 –223

x+1

Warm-Up ExercisesYOU TRY for Examples 3 and 4

Graph the function. State the domain and range.

5. g(x) = –3 +434

x – 5

Warm-Up ExercisesYOU TRY for Examples 3 and 4

6. SNOWMOBILE The value of a snowmobile has been decreasing by 7% each year since it was new. After 3 years, the value is $3000. Find the original cost of the snowmobile.

$3729.69SOLUTION

Warm-Up ExercisesKEEP GOING

ANSWER

domain: all real numbers range: y > 0

12

x1. Graph y = 4 . State the domain and range.

Warm-Up ExercisesKEEP GOING

ANSWER

domain: all real numbers range: y > 2

2. Graph y = 3 +2 . State the domain and range.

14

x+2

Warm-Up ExercisesKEEP GOING

3. A new laptop computer costs $1500. The value of the computer decreases by 22% each other.

a. Estimate the value of the computer after 2 years.

b. Estimate when the computer will be worth $550.

ANSWER about $ 913

ANSWER after about 4 yr