Name _________________________________ Date ____________________________ Period _______ Pre-Calculus
Chapter 3 Review – Solutions (
Use
)
or
1) Find the accumulated value of an investment of $1000 at 10% compounded semiannually for 8 years. (
) ( )
(
)
2) Find the accumulated value of an investment of $250 at 3.5% compounded quarterly for 5 years. (
) ( )
(
)
3) Find the accumulated value of an investment of $7000 at 8% compounded continuously for 3 years. (
Write the equation in its equivalent exponential form. 4) 5)
Write the equation in its equivalent logarithmic form. 6) √ 7)
Evaluate the expression without using a calculator. 8) 9) 10)
√
)( )
Name _________________________________ Date ____________________________ Period _______ Pre-Calculus Expand each logarithm. Where possible, evaluate logarithmic expressions. 11)
(
)
12)
( )
13)
( )
√
Condense the logarithmic expression into a single logarithm whose coefficient is 1. Where possible, evaluate logarithmic expressions. ( )
14) 15) 16)
(
)
(
)
(
)
Use common logarithms or natural logarithms and a calculator to evaluate to three decimal places. 17) 18)
Solve the exponential equation in terms of natural logarithms. Then give an approximation to three decimal places. 19) (
20)
)
Name _________________________________ Date ____________________________ Period _______ Pre-Calculus 21)
(
)
Solve the logarithmic equation. Be sure to reject any value of number or the logarithm of 0. 22)
(
) (
(
23)
that produces the logarithm of a negative
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(
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) [( )( (
)] ) (
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√(
)
( (
) ) (
( )(
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( ) √ Since √
,
√
. Substituting this into the original equation would result in taking a
logarithm of a negative number, so (
24)
√
is not a solution. The only solution is
) (
) (
) (
( Since
)(
does not check, the only solution is
)
) .
√
.
Name _________________________________ Date ____________________________ Period _______ Pre-Calculus Solve the word problem. 25) The long jump record, in feet, at a particular school can be modeled by ( ) ( ), where is the number of years since records began to be kept at the school. What was the record for the long jump 18 years after records started being kept? ( ) ( ) 26) The population of a particular country was 26 million in 1983; in 1992, it was 32 million. The exponential growth function describes the population of this country years after 1983. Find to three decimal places.
(
)
27) The half-life of the radioactive element plutonium-239 is 25,000 years. A rock was found containing 1.8 grams of plutonium-239. Based on the mass and composition of the rock, a geologist concludes that it originally had 9.3 grams of plutonium-239. How old is the rock?
(
)
(
) (
)
28) A biologist is experimenting with bacteria. She starts with a culture of 100 bacteria and incubates it. If its exponential growth rate is 50% per hour, how many bacteria will there be after 1 day (24 hours)? (
)
29) The function ( ) models the percentage of married men in the United States who were employed t years after 1959. According to the model, what percent of married men are currently employed? In 2016, ( )
Name _________________________________ Date ____________________________ Period _______ Pre-Calculus 30) Prehistoric cave paintings were discovered in the Lascaux cave in France. The paint contained 15% of the original amount of Carbon-14. Estimate the age of the paintings at the time of the discovery. The half-life of Carbon-14 is 5730 years. (
)
31) The August 1978 issue of National Geographic described the 1964 find of dinosaur bones of a newly discovered dinosaur weighing 170 pounds, measuring 9 feet, with a 6-inch claw on one toe of each hind foot. The age of the dinosaur was estimated using potassium-40 dating of the rocks surrounding the bones. Analysis of the rocks indicated that 94.5% of the original amount of potassium-40 was still present. The half-life of potassium-40 is 1.3 billion years. Estimate the age of the dinosaur bones. (
)
32) The population of the city of San Diego was 1,223,400 in 2000. In 2006, it was 1,256,951. Write an exponential model that describes the growth of San Diego, and then use that model to estimate the current population of San Diego.
(
)
(
) (
For 2016,
)
