Math 150 Exam 3 Review
J. Lewis
1. Find all vertical and horizontal asymptotes of each function.
x
a)
f (x) 
c)
f ( x )  ln( x  2 )
f (x) 
b)
2
3 x  9 x  30
d)
f (x)  5  e
25  x
2
2
3 x  9 x  30
x
e)
f (x) 
1 e
x
1 e
x
2. Each function is an exponential function, f ( x )  ab x . Find the formula that fits the
given points for each.
a) f(2)=20 and f(3)=30
3. a) If b c  25
b) f(1)=10 and f(3)=0.4
then what is log
b
5?
b) If log b 100  c then what is b c 2 ?
c) f ( x )  3 e x
Find f
1
( 21 ) .
4. A population had 250 thousand individuals in the year 2000. The population grew
exponentially so that in the year 2010 there were 300 thousand individuals. If the same
growth rate continues,
a) find the formula for the population size after t years past 2000.
b) find the doubling time.
c) find the continuous growth rate.
5. An investment of $20,000 grows at the continuous compound interest rate of 3.5% per
year. The interest rate is the continuous growth rate.
How many years will it take for the amount in the investment to reach $30,000?
6. Solve for x.
a)
x
4 2
x3
 12  0
b)
1
2
c)
e
4x
 3e
2x
 10  0
ln( x  2 )  ln x  ln 3
7. Solve for all (x, y).
a)
2 x  4 y  11
5 x  3 y  3
b)
x y 6
c)
4 x  3 y  12
and
6 x  4 . 5 y  10
d)
4 x  3 y  12
and
6 x  4 . 5 y  18
and
2x  3y  7
and
8. Find all values of k to meet the given condition or state no such k exists.
a)
2x  3y  6
b)
4x  6y  k
c)
kx  3 y  16
has no solution
d)
5 x  4 y  12
3x  2 y  7
6 x  ky  14
has infinitely
has infinitely
many solutions
many solutions
9x  6y  8
kx  8y  10 has no solution
9. Find the intersections point or points in each case. Sketch the graphs.
a) The circle centered at (0, 0) of radius 1 and the circle centered at (2, 1) of radius 2.
b) The ellipse x 2 
y
2
9
 1 and the circle centered at(0, 1) of radius 1.
c) The circle centered at (2, 1) of radius 10 and the line y = 3x+1.
10. Evaluate without a calculator.
a)
2 
sin  
8
b)
2  
cos 

 12 
11. A right triangle has base angle t and base equal to 3, height equal to 1. Find each of
the following:
a)
sin t
b)
f)


sin   t 
2

cos t
c)
 t 
cos  
2
d)
tan t
e)
sec t
12.
Solve for all t in [ 0 , 2  ] for which
a) 2 sin
2
t  2  cos t
b)
tan
:
2
t  sec
2
t30
13. Graph each of the functions sin t , cos t , tan t and sec t .
Be able to fill in a table showing their values at the basic angles.