Intermediate Algebra (11th edition)

(a) 1900

Because xrepresents the number of years since 1750,

Given function

Let

Use a calculator.

The concentration in 1900 was about 309 parts per million.

(b) 1950

Use a calculator.

The concentration in 1950 was about 325 parts per million. NOW TRY

Applying an Exponential Decay Function

The atmospheric pressure (in millibars) at a given altitude x, in meters, can be ap-

proximated by the function defined by

for values of xbetween 0 and 10,000.

Because the base is greater than 1 and the coefficient of xin the exponent is negative,

function values decrease as xincreases. This means that as altitude increases,

atmospheric pressure decreases. (Source:Miller, A. and J. Thompson, Elements

of Meteorology,Fourth Edition, Charles E. Merrill Publishing Company.)

(a)According to this function, what is the pressure at ground level?

Let

The pressure is 1038 millibars.

(b)Approximate the pressure at 5000 m. Round to the nearest unit.

Let

Use a calculator.

The pressure is approximately 531 millibars. NOW TRY

ƒ 150002 L 531

ƒ 150002 = 10381 1.000134 2 -^5000 x=5000.

= 1038

= 1038112 a^0 = 1

ƒ 102 = 10381 1.000134 2 -^0 x=0.

ƒ 1 x 2 = 10381 1.000134 2 - x,

EXAMPLE 7

ƒ 12002 L325 parts per million

ƒ 12002 = 2661 1.001 2200 x= 1950 - 1750 = 200

ƒ 11502 L309 parts per million

ƒ 11502 = 2661 1.001 2150 x=150.

ƒ 1 x 2 = 2661 1.001 2 x

x= 1900 - 1750 = 150.

SECTION 10.2 Exponential Functions 585

NOW TRY
EXERCISE 6
Use the function in Example 6
to approximate, to the nearest
unit, the carbon dioxide con-
centration in 2000.

NOW TRY ANSWERS
6.342 parts per million

NOW TRY
EXERCISE 7
Use the function in Example 7
to approximate the pressure at
6000 m. Round to the nearest
unit.

7.approximately 465 millibars

Complete solution available
on the Video Resources on DVD

10.2 EXERCISES

Concept Check Choose the correct response in Exercises 1–3.

1.Which point lies on the graph of?

A. B. C. D.

2.Which statement is true?

A.The point lies on the graph of.

B.For any , the graph of falls from left to right.

C.The y-intercept of the graph of is.

D. The graph of y= 4 xrises at a faster rate than the graph of y= 10 x.

ƒ 1 x 2 = 10 x 1 0, 10 2

a 71 ƒ 1 x 2 =ax

A^12 ,^25 B ƒ^1 x^2 =^5 x

a 23 ,

1

3

1 1, 0 2 1 3, 1 2 1 0, 1 2 b

ƒ 1 x 2 = 3 x

At ground

level, x=0.