6.3 Exponential Function
MATH 161
TEAGUE
Ex 1) Is the function linear, exponential, or neither?
To check linear: check slope on two set of points
1−11
0−1
=
11−121
1−2
−10
−1
= 10
−110
=
−1
= 110 no
To check exponential:
𝑓(𝑥+1)
𝑓(𝑥)
X
-1
0
1
2
3
f(x)
1/11
1
11
121
1331
= 𝑎 𝑤ℎ𝑒𝑟𝑒 𝑓(𝑥 ) = 𝑁𝑎 𝑥 𝑎𝑛𝑑 𝑓(𝑥 ) = 𝑁
𝑓(0)
𝑓(−1)
𝑓(1)
𝑓(0)
1
=1
=
11
11
= 11
= 11
1
yes, therefore: f(0) = 1 then f(x) = 11x
Ex 2) Is the function linear, exponential, or neither?
To check linear: check slope on two set of points
13−156
0−1
=
156−1872
1−2
−143
−1
=
= 143
−1716
−1
= 1716 no
To check exponential:
𝑓(𝑥+1)
𝑓(𝑥)
X
-1
0
1
2
3
f(x)
13/12
13
156
1872
22464
= 𝑎 𝑤ℎ𝑒𝑟𝑒 𝑓(𝑥 ) = 𝑁𝑎 𝑥 𝑎𝑛𝑑 𝑓(𝑥 ) = 𝑁
𝑓(0)
13
𝑓(−1)
𝑓(1)
𝑓(0)
= 13
=
165
13
12
= 12
= 12 yes, therefore: f(0) = 13 then f(x)=1312x
Ex 3) Give the functions for the graph:
(0,5)
(1,1)
A. y = 5x
C. y = -5x
E. y = 5x-1
G. y = 51-x
B. y = 5-x
D. y = -5-x
F. y = 5-x-1
H. y =1-5-x
Plug in (0,5) and see what function works
5 = 51-0 works therefore G
Ex 4) f(x) = 3x + 5
3x shifts up 5 units
f(x) = 3x + 5
f(x) = 3x
(1,3)
(0,6)
Make sure to change base
to 6 in the graphing tool box.
(0,1)
Domain: (-,)
Range: (5,)
Horizontal Asymptote
y=5
Ex 5) Solve 4-x = 256
4-x = 44
set exponents equal and solve –x = 4 then x = -4
𝟑
𝟐𝟕
𝟓
𝟏𝟐𝟓
3
( )3
5
Ex 6) Solve ( )𝒙 =
3
( )x =
5
set exponents equal x = 3
𝟐 −𝟓
= 𝟔𝟒𝟐𝒙
2 −5
= 84x
Ex 7) Solve 𝟖𝒙
8x
set exponents equal and solve x2 – 5 = 4x
x2 –4x - 5 =0
(x-5)(x+1)
x = -1,5
𝟐
Ex 8) Solve 𝟒𝟗𝒙 ∙ 𝟕𝒙 = 𝟐𝟒𝟎𝟏𝟐
2
72𝑥 ∙ 7x = 78
set exponents equal and solve 2x+x2 = 8
x2 +2x - 8 =0
(x-2)(x+4)
𝟐
Ex 9) Solve 𝒆𝒙 = 𝒆𝟖𝒙 ∙
2
x = -4,2
𝟏
𝒆𝟏𝟓
−15
ex = e8x ∙ 𝑒
set exponents equal and solve x2 = 8x-15
x2 - 8x + 15 =0
(x-5)(x-3)
x = 3,5
Ex 10) If 6x = 7 then 6-2x = ?
*The -2 means to make it a fraction and square it therefore, x =
𝟏
𝟒𝟗
Ex 11) Suppose that g(x) = 2x + 2
a) What is g(-1)? When x = -1, what is the point on the
graph?
2-1 +2=
5
2
𝟓
(-1, )
𝟐
b) If g(x) = 10, what is x? Give point on the graph.
2x +2=10
2x =8
2x =23 x = 3 (3,10)
Ex 12) D(h) = 9e-0.55h can be used to find the number of
milligrams D of a drug that is in a patient’s bloodstream h
hours after the drug has been administered. How many
milligrams will be present after 1 hour? After 11 hours?
9e-0.55(1) = 5.19
9e-0.55(11) = 0.021