Download Exponential Functions Worksheet and more Essays (high school) Physics in PDF only on Docsity!
Name______________________ Group__________ / 50
Exponential Functions
- Sketch the following functions ( 4 pts)
a) ๐(๐ฅ) = 4 ( 0. 5 )
!"#
โ 4 b) ๐(๐ฅ) = โ 2 ( 2 )
!
- Below are the graphs of 4 exponential functions whose rules are in the form
$(!&')
For each case, determine the signs of parameters a and b when 0 < ๐ < 1 ๐๐๐ ๐ > 1
Graph 1 Graph 2 Graph 3 Graph 4
when 0 < c < 1 a =
b =
a =
b =
a =
b =
a =
b =
when c > 1 a =
b =
a =
b =
a =
b =
a =
b =
- Points (0.5, 3.2) and (-1, 0.05) belong to an exponential function in the form of y = ac
x
Find the rule. (2 pts)
- For each of the three functions below, state the range; whether the function is increasing or
decreasing; whether it has a zero (not the value); the y-intercept & the equation of the
asymptote. (4 pts)
Range Increasing
Decreasing?
Zero?
(Y or N)
Y-intercept Asymptote
- Solve the following exponential functions (16 pts)
a) 5
&)(!"*)
b) โ 7
!
,
c) ( โ
!"+
d) 2
!&)
!")
e) 4
!
!
&-
= 1 f) 2 ร 2
!
!
&.
!
g) 0.25( 5 )
!
h) 2 7
!")
x
f x
2 8
x
g x
2
รท
รธ
รถ
รง
รจ
รฆ
x
h x
- In 1960 Adrienne bought a new convertible for $8000. Over the next 6 years, her car
depreciated each year by 15% of the previous yearโs value. During the next 4 years, the value of
the car remained the same. Then because it was so rare & beautiful, her car was classified as a
collectorโs item. From this point on, the value of her shiny old convertible increased by 10% each
year.
What was the value of the car 30 years after it was purchased? (4 pts)
- Given f(x) = ac
x โ h
- k where c>1 and a<0, b<0, k>0 and h>0 ( 4 pts)
State whether the function is increasing or decreasing.
State the range.
State the domain.
