Math 12 '- Precalculus '- Exponential And Logarithm Functions Test - 2009
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3Math 12 – Precalculus – Exponential and Logarithm Functions Test – Fall ’09 NAME________________
Write all responses on separate paper. Show all work for credit. You will need a scientific calculator.
−
+
=
1
x
/ 2
1. Rewrite the equation
3.98 10
10
in equivalent logarithmic form, then solve for x .
Use a calculator to approximate x to the nearest ten thousandth.
(
)
−
−
=
2. Rewrite the equation
8 4 log
x
2
6.09
in equivalent exponential form, then solve for x .
Use a calculator to approximate x to the nearest ten thousandth.
3. Solve the equation for x . Approximate to the nearest thousandth.
−
=
×
x
11
a.
10
6.67259 10
=
x
/24
b.
1.01
7
4. Use properties of logarithms to solve the equation. Approximate to 4 digits if appropriate.
( )
(
)
+
−
=
a.
log
x
log 44 3
x
7
2
2
⎛
⎞
10
( )
+
=
⎜
⎟
b.
log
log 1
0.5
⎝
⎠
2
9x
( )
f x = +
x
5. Given
1 1.322
.
( )
−
=
1
a. Find a formula for the inverse function,
y
f
x
.
( )
b. Find the intercept and asymptote of
f x .
( )
−
1
c. Find the intercept and asymptote of
f
x
.
−
x
2 0 2 4 6 8 10
d. Complete the table
and use the results to sketch a graphing
( )
f x
( )
( )
−
=
=
1
showing
y
f x
and
y
f
x
together and illustrating the symmetry through y = x.
6. Suppose the Gorkon population on planet Xorda in April of 1999 was 1380, and it is estimated that the
population will increase by 2% every 400 years.
a. Assuming a natural growth model for the Gorkons, when will its population have grown to 2000?
b. By what percentage will the population grow in 1800 years?
7. If $300 is invested at 3.65% annual interest rate compounded daily, how long will it take to reach a
value of $500?
×
8
8. Actinium has a half life of about
7.04 10
years. How long will it take a 1 gram sample to decay to
one milligram (one thousandth of a gram).
( )
= i ) which passes through the points (2,5) and
x
9. Find an exponential function (of the form
f x
a b
(5,8). What is the value of f(8) ?
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