Lecture 10 section 4.1 and 4.2 exponential functions
-
Upload
njit-ronbrown -
Category
Technology
-
view
128 -
download
2
Transcript of Lecture 10 section 4.1 and 4.2 exponential functions
![Page 1: Lecture 10 section 4.1 and 4.2 exponential functions](https://reader036.fdocuments.in/reader036/viewer/2022081419/55615e3ad8b42a654b8b49f2/html5/thumbnails/1.jpg)
MATH 108
Sections 4.1-4.2
Exponential Functions
![Page 2: Lecture 10 section 4.1 and 4.2 exponential functions](https://reader036.fdocuments.in/reader036/viewer/2022081419/55615e3ad8b42a654b8b49f2/html5/thumbnails/2.jpg)
The term 27 is called a power. If a number is in exponential form, the exponent represents how many times the base is to be used as a factor.
7
ExponentBase
2
![Page 3: Lecture 10 section 4.1 and 4.2 exponential functions](https://reader036.fdocuments.in/reader036/viewer/2022081419/55615e3ad8b42a654b8b49f2/html5/thumbnails/3.jpg)
3© 2010 Pearson Education, Inc. All rights reserved
RULES OF EXPONENTS
Let a, b, x, and y be real numbers with a > 0 and b > 0. Then
,x y x ya a a
,x
x yy
aa
a
,x x xab a b
,yx xya a
0 1,a
1 1.
xx
xa
a a
![Page 4: Lecture 10 section 4.1 and 4.2 exponential functions](https://reader036.fdocuments.in/reader036/viewer/2022081419/55615e3ad8b42a654b8b49f2/html5/thumbnails/4.jpg)
![Page 5: Lecture 10 section 4.1 and 4.2 exponential functions](https://reader036.fdocuments.in/reader036/viewer/2022081419/55615e3ad8b42a654b8b49f2/html5/thumbnails/5.jpg)
![Page 6: Lecture 10 section 4.1 and 4.2 exponential functions](https://reader036.fdocuments.in/reader036/viewer/2022081419/55615e3ad8b42a654b8b49f2/html5/thumbnails/6.jpg)
![Page 7: Lecture 10 section 4.1 and 4.2 exponential functions](https://reader036.fdocuments.in/reader036/viewer/2022081419/55615e3ad8b42a654b8b49f2/html5/thumbnails/7.jpg)
![Page 8: Lecture 10 section 4.1 and 4.2 exponential functions](https://reader036.fdocuments.in/reader036/viewer/2022081419/55615e3ad8b42a654b8b49f2/html5/thumbnails/8.jpg)
![Page 9: Lecture 10 section 4.1 and 4.2 exponential functions](https://reader036.fdocuments.in/reader036/viewer/2022081419/55615e3ad8b42a654b8b49f2/html5/thumbnails/9.jpg)
![Page 10: Lecture 10 section 4.1 and 4.2 exponential functions](https://reader036.fdocuments.in/reader036/viewer/2022081419/55615e3ad8b42a654b8b49f2/html5/thumbnails/10.jpg)
10© 2010 Pearson Education, Inc. All rights reserved
EXAMPLE 6 Sketching Graphs
Use transformations to sketch the graph of each function.
3 4xf x a.
State the domain and range of each function and the horizontal asymptote of its graph.
1 3xf x b.
3xf x c. 3 2xf x d.
![Page 11: Lecture 10 section 4.1 and 4.2 exponential functions](https://reader036.fdocuments.in/reader036/viewer/2022081419/55615e3ad8b42a654b8b49f2/html5/thumbnails/11.jpg)
![Page 12: Lecture 10 section 4.1 and 4.2 exponential functions](https://reader036.fdocuments.in/reader036/viewer/2022081419/55615e3ad8b42a654b8b49f2/html5/thumbnails/12.jpg)
![Page 13: Lecture 10 section 4.1 and 4.2 exponential functions](https://reader036.fdocuments.in/reader036/viewer/2022081419/55615e3ad8b42a654b8b49f2/html5/thumbnails/13.jpg)
Note that the graph of ex is between 2x and 3x, because 2<e<3. In the first quadrant, 2x<ex<3x; in the second quadrant, 3x<ex<2x. All 3 graphs pass through (0,1).
![Page 14: Lecture 10 section 4.1 and 4.2 exponential functions](https://reader036.fdocuments.in/reader036/viewer/2022081419/55615e3ad8b42a654b8b49f2/html5/thumbnails/14.jpg)
![Page 15: Lecture 10 section 4.1 and 4.2 exponential functions](https://reader036.fdocuments.in/reader036/viewer/2022081419/55615e3ad8b42a654b8b49f2/html5/thumbnails/15.jpg)
43 -1 2 13
Solve each exponential equation.1
(a) 2 32 (b) x x xx
e ee
![Page 16: Lecture 10 section 4.1 and 4.2 exponential functions](https://reader036.fdocuments.in/reader036/viewer/2022081419/55615e3ad8b42a654b8b49f2/html5/thumbnails/16.jpg)
Solve:
![Page 17: Lecture 10 section 4.1 and 4.2 exponential functions](https://reader036.fdocuments.in/reader036/viewer/2022081419/55615e3ad8b42a654b8b49f2/html5/thumbnails/17.jpg)
17© 2010 Pearson Education, Inc. All rights reserved
EXAMPLE 8 Bacterial Growth
A technician to the French microbiologist Louis Pasteur noticed that a certain culture of bacteria in milk doubles every hour. If the bacteria count B(t) is modeled by the equation
a. the initial number of bacteria,b. the number of bacteria after 10 hours; andc. the time when the number of bacteria will be
32,000.
with t in hours, find
![Page 18: Lecture 10 section 4.1 and 4.2 exponential functions](https://reader036.fdocuments.in/reader036/viewer/2022081419/55615e3ad8b42a654b8b49f2/html5/thumbnails/18.jpg)
![Page 19: Lecture 10 section 4.1 and 4.2 exponential functions](https://reader036.fdocuments.in/reader036/viewer/2022081419/55615e3ad8b42a654b8b49f2/html5/thumbnails/19.jpg)
![Page 20: Lecture 10 section 4.1 and 4.2 exponential functions](https://reader036.fdocuments.in/reader036/viewer/2022081419/55615e3ad8b42a654b8b49f2/html5/thumbnails/20.jpg)
![Page 21: Lecture 10 section 4.1 and 4.2 exponential functions](https://reader036.fdocuments.in/reader036/viewer/2022081419/55615e3ad8b42a654b8b49f2/html5/thumbnails/21.jpg)
Find the amount A that results from investing a principal P of $2000 at an annual rate r of 12% compounded continuously for a time t of 3 years.