The GPS Advanced Algebra form serves as a comprehensive tool designed to test a variety of concepts centered around exponential growth and decay, utilizing real-world scenarios to elucidate these mathematical principles. From calculating the future balance of a bank account with a given interest rate over a set period to determining the exponential increase in cell phone subscribers in a small town, this form encapsulates a broad spectrum of applications. It encompasses scenarios such as bacterial growth, tournament player eliminations, population modeling, land valuation over decades, and the decay of substances within the body, including medication and caffeine, as well as the depreciation of assets like computers. Moreover, it delves into environmental science by modeling termite population growth. Each question is meticulously crafted to challenge the understanding of exponential functions, pushing students to apply theoretical knowledge to solve practical problems. This not only aids in the grasping of algebraic concepts but also prepares students for real-life situations where exponential growth and decay play crucial roles.
| Question | Answer |
|---|---|
| Form Name | Gps Advanced Algebra Form |
| Form Length | 2 pages |
| Fillable? | No |
| Fillable fields | 0 |
| Avg. time to fill out | 30 sec |
| Other names | decreases, Exponential, gps advanced algebra exponential growth and decay word problems, 1985 |
GPS Advanced Algebra |
Unit 3 |
Name: ____________________ Pd:_____ |
Exponential Growth and Decay Word Problems
1.Find a bank account balance if the account starts with $100, has an annual rate of 4%, and the money left in the account for 12 years.
2.In 1985, there were 285 cell phone subscribers in the small town of Centerville. The number of subscribers increased by 75% per year after 1985. How many cell phone subscribers were in Centerville in 1994?
3.Bacteria can multiply at an alarming rate when each bacteria splits into two new cells, thus doubling. If we start with only one bacteria which can double every hour, how many bacteria will we have by the end of one day?
4.Each year the local country club sponsors a tennis tournament. Play starts with 128 participants. During each round, half of the players are eliminated. How many players remain after 5 rounds?
5.The population of Winnemucca, Nevada, can be modeled by P=6191(1.04)t where t is the number of years since 1990. What was the population in 1990? By what percent did the population increase by each year?
6.You have inherited land that was purchased for $30,000 in 1960. The value of the land increased by approximately 5% per year. What is the approximate value of the land in the year 2011?
7.During normal breathing, about 12% of the air in the lungs is replaced after one breath. Write an exponential decay model for the amount of the original air left in the lungs if the initial amount of air in the lungs is 500 mL. How much of the original air is present after 240 breaths?
8. A adult takes 400 g of i uprofe . Ea h hour, the a ou t of i uprofe i the perso ’s syste de reases by about 29%. How much ibuprofen is left after 6 hours?
9.You deposit $1600 in a bank account. Find the balance after 3 years for each of the following situations:
a.The account pays 2.5% annual interest compounded monthly.
b.The account pays 1.75% annual interest compounded quarterly.
c.The account pays 4% annual interest compounded yearly.
10.You buy a new computer for $2100. The computer decreases by 50% annually. When will the computer have a value of $600?
11.You drink a beverage with 120 mg of caffeine. Each hour, the caffeine in your system decreases by about 12%. How long until you have 10mg of caffeine?
12.The foundation of your house has about 1,200 termites. The termites grow at a rate of about 2.4% per day. How long until the number of termites doubles?