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Exponential Growth
Compound Interest
Exponential Decay
Vocabulary
Formulas
100
Ms. Acosta received a job as a teacher with a starting salary of $34,000. According to her contract, she will receive a 1.5% increase in her salary every year. How much will Ms. Acosta earn in 7 years?
Ms. Acosta will earn about $37,734.73 in 7 years
100
Theo invested $6600 at an interest rate of 4.5% compounded monthly. Determine the value of his investment in 4 years.
The value of Theo’s investment in 4 years is about $7898.97.
100
In the years from 2010 to 2015, the population of the District of Columbia is expected to decrease about 0.9% annually. in 2010, the population was about 530,000. what is the population of the district of Columbia expected to be in 2015?
Your formula should be y=530,000(1-0.009)^5 In 2015, the population is expected to be 506, 575.
100
Define compound interest in your own words.
Interest earned or paid on both the initial investment and previously earned interest, the value added to the principal.
100
What does the r value stand for in all three formulas, and how do you write it?
The rate, represented as a decimal.
200
The number of people who own computers has increased 23.2% annually since 1990. If half a million people owned a computer in 1990, predict how many people will own a computer in 2015.
About 92,095,349 people will own a computer in 2015.
200
Brooke is saving money for a trip to the Bahamas that costs $295.99. She puts $150 into a savings account that pays 7.25% interest compounded quarterly. Will she have enough money in the account after 4 years? Explain.
No, Brooke will have about $199.94 in the account in 4 years.
200
In 2000, 2200 students attended Springdale High. The enrollment has been declining 2% each year. If this trend continues, how many will be enrolled in 2015?
The enrollment of Polaris High School will be about 1,624 in 2015
200
Define exponential growth in your own words.
A quantity that increases at a fixed percent at regular intervals.
200
What is the formula for compound interest?
A=P(1+r/n)^nt
300
The population of Johnson City in 2005 was 25,000. Since then, the population has grown at an average rate of 3.2% each year. What will be the population in 2015?
The population will be about 34,256 people.
300
The Smiths have $12,000 in a savings account. The bank pays 3.5% interest on savings accounts, compounded monthly. Find the balance in 3 years.
In three years, the balance of the account will be $13,326.49.
300
A swimming pool holds a maximum of 20,500 gallons of water. It evaporates at a rate of 0.5% per hour. The poor currently contains 19,000 gallons of water. Write an exponential function w(t) to express the amount of water remaining in the pool after time t where t is the number of hours after the pool reached 19,000 gallons.
w(t) = 19,000(0.995)^t
300
Define exponential decay in your own words.
A quantity that decreases by a fixed percent at regular intervals.
300
What is the formula for exponential growth?
y=a(1-r)^t
400
Brooke is playing a video game in which she establishes and builds up a city. The population of this city is currently 86,000 people, a number that increases by 10% every year. What will the population be in 11 years?
The formula you should use is y = 86,000(1 + 0.1)^11. In 11 years, the population will be 245, 368 people.
400
Marta deposited $80 in a savings account earning 5% interest, compounded annually. How much interest will she earn in 3 years?
The formula you should use is A=80(1+0.05/1)^3(1) Marta will earn $12.61 in interest after 3 years.
400
A pot of soup, currently 25°C above room temperature, is left out to cool. If that temperature decreases by 10% per minute, then what will the difference be in 9 minutes? If necessary, round your answer to the nearest tenth.
The formula you should use is y=25(1 – 0.1)^9. The difference in temperature will be about 9.7°C.
400
Why do you think it is called "growth" and "decay"?
It is exponential growth because the quantity is increasing, or "growing". Exponential decay can be thought of as the value "decaying" as it gradually decreases.
400
What is the formula for exponential decay?
y=a(1-r)^t