MATH 1914Exam #3 Review (2.7 – 3.5)
Solve each inequality below by determining the boundary points and using a sign chart.
State your solutions in interval notation.
1. 2.
3. 4.
Determine the domain of each function below algebraically. Show your work!
5. 6.
7.
Graph each function below by creating a table of coordinates.
8. 9.
Describe how the graph of each function below would differ from the graph of . Also state the horizontal asymptote of each.
10. 11. 12.
Use the appropriate compound interest formula below to answer problems 6-9.
13. Find the accumulated value of an investment of $5000 for 20 years at an interest rate of 3.8%
if the interest is compounded
a) annuallyb) quarterlyc) dailyd) continuously
14. The day a baby is born, her grandmother invests some money in an account which pays 4.5%
interest compounded continuously. On her granddaughter’s 21st birthday, she presents her
with a check for $10,000. How much did the grandmother invest?
15. An investment of $20,000 is invested at an interest rate of 3%, compounded annually. How
long does it take for the investment to grow to $50,000?
16. Find the interest rate required for an investment to double in 40 years if it is compounded
semi-annually.
17. The function describes the percentage of information that a particular
person remembers x weeks after learning the information.
a) Determine the percentage of information that is remembered after 2 weeks.
b) After how many weeks does the person remember only 25% of what they learned?
Rewrite each equation in its equivalent exponential form, and solve for x, if possible.
18. 19. 20.
Rewrite each equation in its equivalent logarithmic form.
21. 22. 23.
Evaluate each logarithmic expression.
24. 25. 26.
27. 28. 29.
State the domain of each function below.
30. 31. 32.
Use properties of logarithms to expand each logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions.
33. 34. 35. 36.
Use properties of logarithms to condense each logarithmic expression. Write each expression as a single logarithm whose coefficient is 1.
37. 38. 39.
Use the change of base property to evaluate each logarithm to four decimal places.
40. 41. 42.
Solve each exponential equation algebraically. Show your work, and give both an exact answer and a decimal approximation, rounded to the nearest thousandth.
43. 44. 45.
46. 47. 48.
Solve each logarithmic equation algebraically. Show your work, and check your answers!
49. 50. 51.
52. 53.
54. 55.
56. The formula models the population of Sometown, USA at time t, where t is the
number of years after 1950.
a) What was the population of Sometown in the year 1950?
b) What was the population of Sometown in the year 2000?
c) In what year did the population of Sometown reach 80,000?
57. The function models the percentage of students who could recall the
important features of a classroom lecture as a function of time, where x represents the number
of days that have elapsed since the lecture was given.
a) What percentage of the students recall important features of the lecture after 3 days?
b) When do only half of the students recall the important features of the lecture?
58. The population of Colombia was 44.4 million in the year 2007, and it is projected to reach 55.2
million in the year 2025. Determine the growth rate, k, to 4 decimal places, and write a
function of the form to model the population of Colombiat years after 2007.
59. The half-life of Potassium-40 is approximately 1.31 billion years. Determine the decay rate, k,
to 4 decimal places, and write a function of the form to model the amount of
Potassium-40 present after t billion years.
60. A substance decreases from 100 grams to 75 grams in 24 hours. Determine the half-life of the
substance.
61. A bird species in danger of extinction has a population that is decreasing exponentially. In the
year 2000 the population was 1600, and in the year 2010 the population is only 600. When the
population drops below 100, the situation will be irreversible. When will this happen?