Worksheet Math 155 KEY
https://www.math.wvu.edu/155/eng/
1 of 2
Group 7 (Sec 3.1.)
Work in groups. 5 points.
There are three questions in all. Note that question 3 has two parts.
The worksheet is about exponents and the exponential functions
x
a
You are required to read page 142 and part of 143 of the text.
1. Say what 1n
bmeans whennis a positive integer and bis a positive real
number. 1
. ... . . .
nth n
nnn
n
aa aa a b n a a b b== == =
๎๎๎๎๎
times
Let Taking the root of both sides gives:
2. What does mn
b mean when
n
and
m
are positive integers and bis a positive real
number?
()
1 111 11
times
. . ... .
mm
n nnn nn n
m
b bbb bb b==
๎๎๎๎๎๎๎๎๎
3. Read page 142 and the top of 143 of the book to the result labeled 1. lim rx
rx
aa
โ
=
.
3.a At the top of page 143, the author says โWe know what 1.7 1.8
2 and 2 mean.โ
Estimate 1.8
2 without a calculator (This is what he means when he says โWe knowโ).
(
)
()
4
18 9 44
1
1.8 1 5
10 5 5 5
4
1.8 5
5
5
22 22 2.22.2
2 " 2. 2 ."
24.
2.ab
+
=== = =
<<
So "Estimate means "Estimate Do this in three steps:
First estimate the value of , then raise it to the power . Finally multiply that by 2
R
() ()
55
55
55
2
1.1, 1.2
1.1 1.61051 2 2.48832 1.2
ab
ab
ab
<<
==
== << ==
aising each term to the fifth power gives:
It seems reasonable to start with:
Inputting these values gives:
That works, so now take the fifth root
()
55 5
4
2 1.1 2 1.2, 2 1.1 1.2 1.15
4
1.15
th
ab<<โ<< โ
=
of each term to get back to the original inequality:
And we see that lies between and , so say
We don't need a calulator to raise this to the power. Notice:
()
()
()
2
22
1.8
1.15 1.3325 1.749
2. 2*1.749 3.498
2 3.4822 3.498 3.4822 0.014, 0.4%
=โ
=
โโ โ
Finally multiply this by
Note: Value of is so the error on the estimate is only i.e.
