Transcript Analysis and Applications - Northland Preparatory Academy

Analysis and
Applications
in Section 3.4b
HW: p. 317-318 39, 41,
47, 49, 53
Last class we discussed how the graph of every logarithm func.
is a stretch or shrink of the graph of the natural logarithm func…
Now let’s analyze our new function!!!
f  x   logb x, b  1
Domain:
(b, 1)
(1, 0)
Range: All reals
Continuous
Increasing on D
No Symmetry
Unbounded
No Local Extrema
V.A.:
 0,
x0
No Horizontal Asymptotes
E.B.:
lim f  x   
x 
Quality Practice Problems
Graph the given function, and analyze it for domain, range,
continuity, inc./dec. behavior, asymptotes, and end behavior.
ln  9 x 
f  x   log1 3 9x  
ln 1 3
Domain:
 0,
Continuous
Asy:
x0
Range:
 , 
Always Decreasing
E.B.:
lim f  x   
x 
Quality Practice Problems
Graph the given function, and analyze it for domain, range,
continuity, inc./dec. behavior, asymptotes, and end behavior.
h  x   ln  x
Domain:
 0,
Continuous
Asy:
x0
3
Range:

 , 
Always Increasing
E.B.:
lim h  x   
x 
Quality Practice Problems
The Richter scale magnitude R of an earthquake is based
on the features of the associated seismic wave and is
measured by
R  log  a T   B
where a is the amplitude in micrometers, T is the period
in seconds, and B accounts for the weakening of the
seismic wave due to the distance from the epicenter.
compute the earthquake magnitude R for each set of values.
(a)
a  250, T  2, B  4.25
250
R  log
 4.25  6.347
2
Quality Practice Problems
The Richter scale magnitude R of an earthquake is based
on the features of the associated seismic wave and is
measured by
R  log  a T   B
where a is the amplitude in micrometers, T is the period
in seconds, and B accounts for the weakening of the
seismic wave due to the distance from the epicenter.
compute the earthquake magnitude R for each set of values.
(b)
a  300, T  4, B  3.5
300
R  log
 3.5  5.375
4
Another guided practice…
The relationship between intensity I of light (in lumens) at a
depth of x feet in Lake Superior is given by
I
log  0.0125 x
12
What is the intensity at
a depth of 10 ft?
Plug in x = 10, solve for I:
I
log  0.0125 10 
12
I
0.125
 10
12
0.125
I  12 10
 8.999 lumens
Whiteboard Problems…
Solve for x:
1.2  log1.2 x
x
Solve graphically!!!
 1.258  x  14.767
Whiteboard Problems…
Solve for x:
ln x  x
3
Solve graphically!!!
 6.406  x  93.354