Algebra II : Mathematical Relationships and Basic Graphs
Study concepts, example questions & explanations for Algebra II
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Example Questions
Example Question #311 : Exponents
Sheila wants to double her initial investment into a compounded interest account, with an interest rate of 4%. How long will this take, if the interest is compounded annually?
0.52 years
1.923 years
0.0565 years
17.67 years
17.67 years
To determine the amount of time needed to double the initial investment - P - into a compound interest account, we simply plug in our given information into the formula:
where B is the balance, P is the initial investment, r is the interest rate (as a decimal), n is the number of times the interest is compounded, and t is the time elapsed.
Now, because we are doubling P, our balance B becomes two times P:
Now, we can solve for P:
To bring the time variable down from being an exponent, we take the logarithm of both sides (common or natural):
Example Question #312 : Exponents
If a person deposits 300 dollars to a savings account, which earns one percent interest that is compounded annually, what is the balance after 60 years?
Write the formula for compound interest.
Substitute all the known values into the formula.
The answer is:
Example Question #313 : Exponents
Suppose Billy's has 
Write the compound interest formula.
where 
Substitute all into the equation.
The answer is:
Example Question #314 : Exponents
Peter opens a savings account on his 
The formula for calculating compount interest is as follows:
where
In this problem, the present value of the money is $5000, and the interest rate is 7%. If Peter takes the money out when he is 50, it would have been compounded 29 times (once per year). Therefore:
Example Question #1 : Radioactive Decay Equations
Over the past few years, the number of students enrolled at a certain university has been decreasing. Each year there is a 12% decrease in student enrollement. Currently, 14,286 students are enrolled. If this trend continues, how many students will be enrolled in 5 years?
This is an exponential decay problem. The formula for exponential decay is:
Where
This problem requests the number of students five years in the future. The rate of decay is twelve percent. Therefore:
Example Question #2 : Radioactive Decay Equations
Sceintists recently discovered a new type of metal compound. They have roughly 15 grams of this compound, which has a half life of 16 hours. Approximately how much of this substance will the scientists have in 24 hours?
Recall the radioactive decay formula:
The half life formula is:
Plug in the given half life:
Plug this value into the radioactive decay formula:
Example Question #1 : Radioactive Decay Equations
The equation for radioactive decay is,
Where 
The half life of Carbon-14 is about 
None of the other answers.
Using the equation for radioactive decay, we get:
Example Question #3 : Radioactive Decay Equations
The number of fish in an aquarium is decreasing with exponential decay. The population of fish is decreasing by 
None of these answers are correct
Every year the population of fish losses 7%. In other words, every year 93% of the fish remain from the previous year. Knowing this, we can use the original number of fish to find the number of fish for the next year. Since we want to know the number of fish 4 years from now, we multiply 1500 by 93% four times.
Example Question #319 : Exponents
The population of a city is decreasing. The city has a population of 
Because the population of the city is decreasing every year at 10.5% we can find the population after each year by using
Because this decrease will continue every year for the 6 years, we can continue to multiply the population by the decay for every year.
Example Question #4 : Radioactive Decay Equations
There is water leaking out of a cup. 
None of these answers are correct
Because the water is leaking at a continuous rate, we can use the exponential decay equation.
To calculate this we must first convert both time to seconds
Our equation is then
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