College algebra help
Please work on each problem on a separate sheet of paper and write your final answer(s) in the blank provided. Write ONLY final answers on this paper.
1. The minimum wage was $5.15 in 1990 and $7.25 in 2009. Find the average rate of change in the minimum wage from 1990 to 2009.
2. Clear County Cable Television charges a $60 installation fee and $44 per month for basic service. Write an equation that can be used to determine the total cost C(t) of t months of basic cable television service. Find the total cost of 1 year of service.
3. The function T given by T(d) = 10d + 20 can be used to determine the temperature T, in degrees Celsius, at a depth d, in kilometers, inside the earth.
a. Find T(5), T(2), and T(1000).
b. The radius of the earth is about 5600 km. Use this fact to determine the domain of the function. Use interval notation.
4. The equation y = 0.08x + 0.83 estimates the number of homeschooled children in the US, in millions, where x is the number of years after 1999. For what years will the number of homeschooled children exceed 2 million?
5. Jessie’s Juice Bar prices its bottled juices by raising the wholesale price 50% and then adding 25 cents. What is the wholesale price of a bottle of juice that sells for $2.95?
6. The score N on a test varies directly as the number of correct responses a. Ellen answers 29 questions correctly and earns a score of 87. What would Ellen’s score have been if she had answered 25 questions correctly?
7. The power P expended by heat in an electric circuit of fixed resistance varies directly as the square of the current C in the circuit. A circuit expends 180 watts when a current of 6 amperes is flowing. What is the amount of heat expended when the current is 10 amperes?
8. Lauren and Cathy leave a campsite, Lauren biking due north and Cathy biking due east. Lauren bikes 7 km/hr slower than Cathy. After 4 hours, they are 68 km apart. Find the speed of each bicyclist.
9. An open box is made from a 10cm by 20cm piece of aluminum by cutting a square from each corner and folding up the edges. The area of the resulting base is 90 square cm. What is the length of the sides of the squares?
10. The function S(t) = -16t2 + 80t + 224 gives the height S, in feet, of a model rocket launched with a velocity of 80 ft/sec from a hill that is 224 ft high, where t is the time, in seconds.
a. Determine when the rocket reaches the ground.
b. On what interval is the height greater than 320 ft?
11. The population P, in thousands, of Novi is given by:
where t is the time, in months. Find the interval on which the population was 400,000 or greater.
12. In 1970, only 4.7% of the US population was foreign-born, while in 2007, 12.6% of the population was foreign-born. The quartic function:
f(x) = -0.0000007623221×4 + 0.00021189064×3 – 0.016314058×2 + 0.2440779643x + 13.59260684
where x is the number of years since 1900, can be used to estimate the percent of the US population for years 1900 to 2007 that was foreign-born. Using this function, estimate the percent of the population that was foreign-born in 1930, 19990, and 2000; then, estimate how many will be foreign born in 2020.
13. Following the birth of twins, the grandparents deposit $16,000 in a college trust fund that earns 4.2% interest, compounded quarterly.
a. Find a function for the amount in the account after t years.
b. Find the amount in the account at t = 0, 12, and 18 years.
14. How long will it take an investment to double if it is invested at 8.6% compounded continuously?
15. The average walking speed w, in feet per second, of a person living in a city of population P, in thousands, is given by the function w(P) = 0.37 ln P + 0.05.
a. The population of Wichita, Kansas is 353,823. Find the average walking speed.
b. A city’s population has an average walking speed of 3.4 ft/sec. Find the population.
16. Cash Social Security distributions were $35 million, or $0.035 billion, in 1940. This amount has increased exponentially to $492 billion in 2004. Assuming that the exponential growth model applies:
a. Find the exponential growth rate k.
b. Find the exponential growth function.
c. Estimate the total cash distributions in 1965 and in 2015.
d. In what year will the cash benefits reach $1 trillion?
17. The value of 75 coins, consisting of nickels and dimes, is $5.95. How many of each kind are there?
18. A dietician must plan a breakfast menu that provides 460 calories, 9 grams of fat, and 55 mg of calcium. One plain bagel contains 200 calories, 2 grams of fat, and 29 mg of calcium. A one-tablespoon serving of peanut butter contains 100 calories, 10 grams of fat, and 24 mg of calcium. One banana contains 105 calories, 1 gram of fat, and 7 grams of calcium. How many servings of each are required to provide the desired nutritional values?
19. A student has a total of 226 on three tests. The sum of the scores on the first and second test exceeds the score on the third test by 62. The first test exceeds the second by 6. Find the three scores.
20. One year, Don invested a total of $40,000, part at 4%, part at 5%, and the rest at 5.5%. The total amount of interest received on the investments was $1990. The interest received on the 5.5% investment was $590 more than the interest received on the 4% investment. How much was invested at each rate?
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