Math 1111- Summer 2013
Score:
Name:
Test 4: Sections 5.1 – 5.6
Directions: ONLY use PENCIL please. Work each of the problems out in the space provided, and show all of
your work. Leave all answers in reduced fraction form. Each problem is worth 5 points.
Solve the problem.
1) A city is growing at the rate of 0.8% annually. If there were 3,980,000 residents in the city in 1995, find how
many (to the nearest ten-thousand) are living in that city in 2000. Use
2)Graph the function. g(x) =
.
3) Graph of f(x) =
Solve the problem.
4) The function
can be used to determine the milligrams D of a certain drug in a patient's
bloodstream h hours after the drug has been given. How many milligrams (to two decimals) will be present
after 9 hours?
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Leave all answers in reduced fraction form unless otherwise stated.
Use the compound interest formula
(
)
to solve. Round to the nearest cent.
5) Find the accumulated value of an investment of $ 1700 at 2% compounded quarterly after 4 years.
Write the equation in its equivalent exponential form.
6)
Write the equation in its equivalent logarithmic form.
7)
Evaluate the expression.
8)
Find the domain of the logarithmic function. Make sure to use interval notation.
9) f(x) =
Evaluate the expression.
10) log 0.001
Solve the problem.
11) Use the formula
( )
to find the intensity R on the Richter scale, given that amplitude a is 443
micrometers, time T between waves is 2.8 seconds, and B is 2.1. Round answer to one decimal place.
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Leave all answers in reduced fraction form unless otherwise stated.
Use properties of logarithms to expand the logarithmic expression as much as possible.
12)
Use common logarithms or natural logarithms and a calculator to evaluate to four decimal places
13)
Solve the equation.
14)
Solve the exponential equation. Round your answer to 2 decimal places.
15)
Solve the logarithmic equation.
16)
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Leave all answers in reduced fraction form unless otherwise stated.
Solve the logarithmic equation.
17) log (x + 5) = log (5x - 4)
Solve the problem.
18) The population of a particular country was 24 million in 1983; in 1995, it was 32 million. The exponential
growth function
describes the population of this country t years after 1983. Find k to three decimal
places.
Solve.
19)
A fossilized leaf contains 28% of its normal amount of carbon 14. How old is the fossil (to the nearest year)? Use
5600 years as the half-life of carbon 14.
Use the formulas
20.) What is the range of f(x) = 2x. Make sure to write your answer in interval notation.
Page 4 of 4
Leave all answers in reduced fraction form unless otherwise stated.