High School
SAT
SAT Elite 1500
SAT Tutoring
ACT
ACT Elite 33
ACT Tutoring
University
MCAT
MCAT Elite 515
Med-School Admissions
Pre-Med Tutoring
Pre-Med Plus
LSAT
LSAT Elite 170
LSAT Self-Paced
LSAT Tutoring
DAT
DAT Elite
DAT Tutoring
Log in
Get Started for Free
Rates of Change
Related Topics
Wize High School Grade 12 Pre-Calculus Textbook > Rates of Change
Rates of Change of Exponential Functions
5 Activities
The instantaneous rate of change for
f
(
x
)
=
2
x
f(x)=2^{x}
f
(
x
)
=
2
x
is
3
2
\dfrac{3}{2}
2
3
.
If
h
=
0.001
h=0.001
h
=
0.001
, what is
x
x
x
?
A)
x
=
log
2
(
0.0015
2
0.001
+
1
)
x=\log_2{\Big(\dfrac{0.0015}{2^{0.001}+1}\Big)}
x
=
lo
g
2
(
2
0.001
+
1
0.0015
)
B)
x
=
log
2
(
0.0015
2
0.001
−
1
)
x=\log_2{\Big(\dfrac{0.0015}{2^{0.001}-1}\Big)}
x
=
lo
g
2
(
2
0.001
−
1
0.0015
)
C)
x
=
log
(
0.0015
2
0.001
−
1
)
x=\log{\Big(\dfrac{0.0015}{2^{0.001}-1}\Big)}
x
=
lo
g
(
2
0.001
−
1
0.0015
)
D)
x
=
log
(
0.0015
2
0.001
+
1
)
x=\log{\Big(\dfrac{0.0015}{2^{0.001}+1}\Big)}
x
=
lo
g
(
2
0.001
+
1
0.0015
)
I don't know
Check Submission
More Rates of Change of Exponential Functions Questions:
Rates of Change
The population of flies is given by
P
(
t
)
=
15
(
5
)
t
/
4
P(t)=15(5)^{t/4}
P
(
t
)
=
15
(
5
)
t
/4
, where
t
t
t
is in weeks.
Rates of Change of Exponential Functions
Practice: Rates of Change of Exponential Functions
If the instantaneous rate of change for the function
f
(
t
)
=
−
6
(
0.45
)
t
2
f(t)=-6(0.45)^{\frac{t}{2}}
f
(
t
)
=
−
6
(
0.45
)
2
t
is
5
5
5
, what is
t
t
t
? Let
h
=
0.001
h=0.001
h
=
0.001
.
Rates of Change of Exponential Functions
Practice: Rates of Change of Exponential Functions
If the instantaneous rate of change for the function
f
(
t
)
=
4
(
1.75
)
t
2
f(t)=4(1.75)^{\frac{t}{2}}
f
(
t
)
=
4
(
1.75
)
2
t
is
13
13
13
, what is
t
t
t
? Let
h
=
0.001
h=0.001
h
=
0.001
.
Rates of Change of Exponential Functions
Practice: Rates of Change of Exponential Functions
The population of a colony of ants increases 3-fold every 2 weeks. If the population of ants starts with 43, then:
Rates of Change of Exponential Functions
Practice: Rates of Change of Exponential Functions
When light passes through water, it loses
10
%
10\%
10%
of its intensity every
25
25
25
meters.
Rates of Change of Exponential Functions
Practice: Rates of Change of Exponential Functions
A ball is bounced and it obtains a maximum height of 8 meters. Every time the ball hits the ground, it reaches
80
%
80\%
80%
of its original height.
Rates of Change of Exponential Functions
Practice: Rates of Change of Exponential Functions
A car depreciates in value once it is driven off the lot. Matija is looking into buying a new car worth
$
60
,
000
\$60,000
$60
,
000
and the car depreciates in value by
3
%
3\%
3%
annually.