4.4: Practice Problems
- Page ID
- 139272
\( \newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} } \)
\( \newcommand{\vecd}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash {#1}}} \)
\( \newcommand{\id}{\mathrm{id}}\) \( \newcommand{\Span}{\mathrm{span}}\)
( \newcommand{\kernel}{\mathrm{null}\,}\) \( \newcommand{\range}{\mathrm{range}\,}\)
\( \newcommand{\RealPart}{\mathrm{Re}}\) \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\)
\( \newcommand{\Argument}{\mathrm{Arg}}\) \( \newcommand{\norm}[1]{\| #1 \|}\)
\( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\)
\( \newcommand{\Span}{\mathrm{span}}\)
\( \newcommand{\id}{\mathrm{id}}\)
\( \newcommand{\Span}{\mathrm{span}}\)
\( \newcommand{\kernel}{\mathrm{null}\,}\)
\( \newcommand{\range}{\mathrm{range}\,}\)
\( \newcommand{\RealPart}{\mathrm{Re}}\)
\( \newcommand{\ImaginaryPart}{\mathrm{Im}}\)
\( \newcommand{\Argument}{\mathrm{Arg}}\)
\( \newcommand{\norm}[1]{\| #1 \|}\)
\( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\)
\( \newcommand{\Span}{\mathrm{span}}\) \( \newcommand{\AA}{\unicode[.8,0]{x212B}}\)
\( \newcommand{\vectorA}[1]{\vec{#1}} % arrow\)
\( \newcommand{\vectorAt}[1]{\vec{\text{#1}}} % arrow\)
\( \newcommand{\vectorB}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} } \)
\( \newcommand{\vectorC}[1]{\textbf{#1}} \)
\( \newcommand{\vectorD}[1]{\overrightarrow{#1}} \)
\( \newcommand{\vectorDt}[1]{\overrightarrow{\text{#1}}} \)
\( \newcommand{\vectE}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash{\mathbf {#1}}}} \)
\( \newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} } \)
\( \newcommand{\vecd}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash {#1}}} \)
1. Write each as a percent:
a. \(\frac{3}{4}\)
b. \(\frac{4}{5}\)
c. \(\frac{7}{10}\)
2. The fraction \(\frac{5}{7}\) is equivalent to what percent? Round your answer to the nearest tenth of a percent.
3. The fraction \(\frac{7}{9}\) is equivalent to what percent? Round your answer to the nearest tenth of a percent.
4. The fraction \(\frac{2}{11}\) is equivalent to what percent? Round your answer to the nearest tenth of a percent.
5. Write each as a percent:
a. 0.23
b. 0.215
c. 1.09
6. Write each as a decimal:
a. \(15 \%\)
b. \(4 \%\)
c. \(7.5 \%\)
7. \(20 \%\) is equivalent to what fraction in reduced terms?
8. \(86 \%\) is equivalent to what fraction in reduced terms?
9. \(58 \%\) is equivalent to what fraction in reduced terms?
10. What number is \(70 \%\) of 40 ?
11. What number is \(45 \%\) of 155 ?
12. 105 is what percent of 225 ?
13. 170 is what percent of 245 ?
14. 18 is \(30 \%\) of what number?
15. 130 is \(65 \%\) of what number?
16. Valerie paid \(\$ 170\) for an item that was originally priced at \(\$ 550\). What percent of the original price did Valerie pay? Round your answer to the nearest tenth of a percent.
17. Trader Joe's sold 8,132 bags of tortilla chips last month. If 7,687 of these bags were fat free, find the percent that were fat free. Round your answer to the nearest percent.
18. \(76 \%\) of the questions on a student's test were correct. There were 50 questions. How many of the questions were correct?
19. At a restaurant, the bill comes to \(\$ 35\). If you decide to leave a \(15 \%\) tip, how much is the tip? Round your answer to the nearest cent.
20. What is the sales tax on a suit priced at \(\$ 295\) if the sales tax is \(7 \%\) ?
21. What is the sales tax on a suit priced at \(\$ 1266\) if the sales tax is \(6 \%\) ?
22. A lender requires a minimum down payment of \(16 \%\) of the value of the home. You have \(\$ 39,000\) cash available to use as a down payment toward a home. Determine the maximum home value that you can finance.
23. The population of a town increased from 3,850 in 2005 to 5,900 in 2012 . By what percent did the population increase?
24. The price of a latte dropped from \(\$ 3.12\) to \(\$ 3.00\). Find the absolute change and relative change of the price of a latte.
25. Theresa's annual income increased from \(\$ 31,000\) to \(\$ 48,000\). Find the absolute change and relative change of Joe's annual income.
26. A shirt that was originally marked as \(\$ 24.95\) rings up at the register as \(\$ 19.96\). What is the percent discount on the shirt?
27. The U.S. Weather Bureau has a station on Mauna Loa in Hawaii that has measured carbon dioxide levels since 1959. At that time, there were 307 parts per million of carbon dioxide in the atmosphere. In 2005, the figure was 391 parts per million. Find the increase in carbon dioxide levels and the percent of increase. Round to the nearest tenth of a percent.
28. Anthony and his son Johnny are exercising more regularly and keeping track of their weight loss. Both Anthony and Johnny lost 10 pounds.
a. From this information alone, can you determine if they both lost the same percentage of weight?
b. Suppose Anthony's starting weight is 190 pounds and Johnny's starting weight is 155 . Who lost a larger percent of their starting weight?
29. A company calls to notify you that the interest rate on your credit card will increase from \(16 \%\) to \(18 \%\).
a. Determine the number of percentage points the interest rate increased by.
b. Determine the percent increase of the interest rate.
30. The sales tax rate for the state of Washington was \(5.7 \%\). If the sticker price of a car in Washington is \(\$ 4,100\), what will be the final cost of the car, including tax?
31. A store is having a \(35 \%\) off sale. If the original price of the shirt is \(\$ 18.00\), what is the price of the shirt after the discount is applied (not including tax)?
32. Hank currently makes \(\$ 13.00\) per hour and is going to receive a \(7 \%\) raise. What will be Hank's new hourly wage?
33. At a restaurant, the bill comes to \(\$ 50\). If you decide to leave a \(15 \%\) tip, what is the total amount you paid?
34. At a restaurant, the bill comes to \(\$ 32.20\). If you decide to leave an \(18 \%\) tip, what is the total amount you paid?
35. Sam lost \(11 \%\) of his body weight after including healthier foods in his diet and exercising regularly. If his original weight was \(218 \mathrm{lbs}\), what is his current weight?
36. A sales clerk received an increase in her annual salary, which is now \(\$ 27,300\). If she received a \(5 \%\) raise, what was her starting salary? Round your answer to the nearest cent.
37. Joyce paid \(\$ 84.50\) for an item at the store that was \(35 \%\) off the original price. What was the original price? Round your answer to the nearest cent.
38. You purchased a new car for a total cost of \(\$ 19,241.94\), which includes the \(13 \%\) sales tax. What was the original price of the car? Round your answer to the nearest cent.
39. Given the function \(f(x)=24(0.72)^x\), evaluate the following.
a. \(f(-3)\)
b. \(f(0)\)
c. \(f(2)\)
40. Given the function \(f(x)=5(1.08)^x\), evaluate the following.
a. \(f(-1)\)
b. \(f(0)\)
c. \(f(3)\)
41. For the function \(f(x)=170(0.8)^x\)
a. Identify the initial value
b. Identify the functions behavior as growth or decay
c. Identify the growth/decay factor
d. Identify the growth/decay rate (as a percent)
42. For the function \(f(x)=5(2)^x\)
a. Identify the initial value
b. Identify the functions behavior as growth or decay
c. Identify the growth/decay factor
d. Identify the growth/decay rate (as a percent)
43. For the function \(h(t)=110(1.3)^t\)
a. Identify the initial value
b. Identify the functions behavior as growth or decay
c. Identify the growth/decay factor
d. Identify the growth/decay rate (as a percent)
44. For the function \(f(x)=60(0.7)^x\)
a. Identify the initial value
b. Identify the functions behavior as growth or decay
c. Identify the growth/decay factor
d. Identify the growth/decay rate (as a percent)
45. Write the exponential function with an initial value of 110 and a growth rate of \(3.5 \%\).
46. Write the exponential function with an initial value of 1504 and a growth rate of \(12 \%\).
47. Write the exponential function with an initial value of 63 and a decay rate of \(28 \%\).
48. Write the exponential function with an initial value of 545 and a decay rate of \(0.4 \%\).
49. Write the exponential function with an initial value of 79 and a growth rate of \(119 \%\).
50. Given the three statements below, identify which represent exponential functions.
a. The number of pennies in your piggy bank doubles every year.
b. The value of a car depreciates at a rate of \(22 \%\) per year.
c. The temperature is decreasing at the rate of \(3^{\circ} \mathrm{F}\) per hour.
51. When a new charter school opened in 2010 , there were 970 students enrolled. Using function notation, write a formula representing the number of students attending this charter school \(t\) years after 2010, assuming that the student population:
a. Increases by 73 students per year
b. Decreases by 36 students per year
c. Decreases by \(9.4 \%\) per year
d. Increases by \(6.1 \%\) per year
e. Remains constant (does not change)
52. A population numbers 1,944 organisms initially and increases by \(5.2 \%\) each year.
a. Write an exponential function for the population of the organisms.
b. Predict the number of organisms after 7 years.
53. A population numbers 17,000 organisms initially and decreases by \(8 \%\) each year.
a. Write an exponential function for the population of the organisms.
b. Predict the number of organisms after 2 years.
54. In 2014 Rose invested \(\$ 16,000\) in a savings account for her newborn son. The account pays \(3.6 \%\) interest each year. Determine the total value of the account in the year 2032, when her son will go to college. Round your answer the nearest cent.
55. You have saved \(\$ 1,000\) to invest in a savings account. Write an exponential function for the value of this investment for each situation that follows:
a. The value increases by \(4 \%\) every year.
b. The value increases by \(4 \%\) every 2 years.
c. The value increases by \(4 \%\) every 6 months.
d. The value increases by \(4 \%\) every 3 months.
56. An investment is initially worth \(\$ 7,400\). Write an exponential function representing the value of this investment after \(t\) years in each of the following situations.
a. The value increases by \(3.6 \%\) every year.
b. The value decreases by \(2 \%\) every year.
c. The value increases by \(11 \%\) every 3 years.
d. The value decreases by \(5 \%\) every 6 months.
57. A new home is purchased for \(\$ 150,000\). The value of the home increases by \(11 \%\) every 2 years. Write an exponential function for the value of the home using time in years as the input quantity.
58. A new home is purchased for \(\$ 200,000\). The value of the home increases by \(1.5 \%\) every 5 years. Write an exponential function for the value of the home using time in years as the input quantity.
59. A new home is purchased for \(\$ 195,000\). The value of the home decreases by \(4 \%\) every 3 years. Write an exponential function for the value of the home using time in years as the input quantity.
60 . A new home is purchased for \(\$ 420,000\). The value of the home decreases by \(8 \%\) every 4 years. Write an exponential function for the value of the home using time in years as the input quantity.