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Find the annual multiplier for the following.
A yearly increase of 5% due to inflation.
A two–bedroom house in Nashville is worth $110,000. If it appreciates at a rate of 2.5% each year, what will it be worth in 10 years?
When will it be worth $200,000?
In Homewood, houses are depreciating at a rate of 5% each year. If a house is worth $182,500 now, how much would it be worth two years from now?
Frank and Alice are penguins. At birth, Frank's beak was 1.95 inches long, while Alice's was 1.50 inches long. If Frank's beak grows by 0.25 inches per year and Alice's grows by 0.40 inches per year, how old will they be when their beaks are the same length?
Tehachapi High School has 839 students and is increasing by 34 students per year. Meanwhile, Fresno High School has 1644 students and is decreasing by 81 students per year. In how many years will the two high schools have the same number of students? Be sure to show all work.
In 1999, Charlie received the family heirloom marble collection, consisting of 1239 marbles. The original marble collection was started by Charlie's great grandfather back in 1905. Each year Charlie's great grandfather had added the same number of marbles to his collection. When he passed them on to his son he insisted that each future generation add the same number of marbles per year to the collection. When Charlie's father received the collection in 1966 there were 810 marbles.
a) How many years has the collection been maintained?
b) How many marbles are added to the collection each year?
c) Use the information you found in part (b) to figure out how many marbles were in the original collection when Charlie's great grandfather started it.
d) Write a generalized expression describing the growth of the marble collection since it was started by Charlie's great grandfather.
e) When will Charlie (or his children) have more than 2000 marbles.
Suppose your parents spend an average of $150 each month for your food. In five years, when you're living on your own, how much will you be spending on food each month if you're eating about the same amount and inflation averages about 4% per year? Write an equation that represents your monthly food bill x years from now if both the rate of inflation and your eating habits stay the same.
Find the multiplier and time for the following.
A yearly increase of 1.23% in population.
The value of a new $15,000 vehicle decreases at 20% per year. Find its value after a year.
Mary was 4' 3 " tall and weighed 85 pounds at the beginning of last year. Now she is 15% taller and 5% heavier. What are her height and weight now?
Frank and Alice are penguins. As youngsters, Frank has a beak that is 2 inches long and Alice has a beak that is 1.5 inches long. Both of their beaks grow at a rate of Z inches per year. After 3 years, Frank's beak is 4 inches long. By how much does each penguin's beak grow per year? How long will Alice's beak be after 3 years?
Brian is twice as old as Judy. Judy is five years younger than Tom. Tom is 15 years old. How old is Brian?
Each year the Strongberg Construction company builds twenty more houses than in the previous year. Last year they built 180 homes. Acme Homes business is increasing by 15% each year and they built 80 homes last year.
a) Assuming that you don't have a graphing calculator with you now, what can you do to solve this problem with just a scientific calculator?
b) Write equations for each construction company and find the year in which both construction companies will build the same number of homes.
Lexington High School has an annual growth rate of 4.7%. Three years ago there were 1500 students at the school.
How many students are there now?
How many students were there 5 years ago?
How many students will be there in n years?
In the first year a tractor manufacturing company produced 75 tractors, which is 45 less than one hundredth of its production after 5 years.
How many tractors were produced in the fifth year?
The value of a new $15,000 vehicle decreases at 20% per year. Find its value after a year.
Macario's salary is increasing by 5% each year. His rent is increasing by 8% each year. Currently, 20% of Macario's salary goes to pay his rent. Assuming that Macario does not move or change jobs, what percent of his income will go to pay rent in 10 years? Think about this problem and if you see a way to solve it, do it. If not, complete the four parts below.
If x represents Macario's current salary write an expression to represent his salary ten years from now.
Use x in an expression to represent Macario's rent now.
Use what you wrote in part (b) to write an expression for the rent ten years from now.
Now use the expressions that you wrote in parts (a) and (c) to write a ratio that will help you answer the question.
Aura currently pays $800 each month to rent her apartment. Due to inflation, however, her rent is increasing by $50 each year. Meanwhile, her monthly take–home pay is $1500 and she predicts that her monthly pay will only increase by $15 each year. Assuming that her rent and take–home pay will continue to grow linearly, will her rent ever equal her take–home pay? If so, when? And how much will rent be that year?
Seven years ago Raj found a box of old baseball cards in the garage. Since then he has added a consistent number of cards to the collection each year. He had 52 cards in the collection after 3 years and now has 108 cards.
a) How many cards were in the original box?
b) Raj plans to keep the collection for a long time. How many cards will the collection contain 10 years from now?
c) Write an expression that determines the number of cards in the collection after n years. What does each number stand for?
Highland has a population of 12,200. Its population has been increasing at a rate of 300 people per year. Lowville has a population of 21,000 but is declining by 250 people per year. Write an equation that represents each city's population over time. What do your variables represent?
You have $5000 in an account that pays 12% annual interest. Compute the amount in the account at the end of one year if:
the interest is compounded annually (once)