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Mathematical Expression Editor
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Practice for simplifying numeric exponentials
How You Can (And Should) Get More Practice!
Below is a few practice problems of various difficulty, but you will need considerably more practice than one each. For that reason
you should definitely use the green “Try Another” button in the top right corner at least two or three times to complete
additional versions of these questions for more practice. You should keep using that button until doing these problems feels straight
forward and easy, and then come back after a week or so of doing other stuff and try again to make sure it is still just as easy for
you.
Theoretically Easier Difficulty Problem
Remember, all exponential growth/decay problems have the same form: (Starting Value)(Growth Multiplier
The starting value is exactly what it sounds, the amount you start with. In this case, it is .
The growth multiplier is how much the value increases each time it changes. In this case, we can get the growth multiplier/factor
from the phrase “”.
The number of cycles is a bit more tricky - you know that the growth factor is applied every , and you want to know the result
after . Use these pieces of information to get how many times the value is multiplied - i.e. the number of growth
cycles.
You are studying a which you know . If you have a container with of your , how many of the would you have after ? (Note you
don’t need to fully calculate the value, just enter the calculation without simplifying)
Theoretically Medium Difficulty Problem
Remember, all exponential growth/decay problems have the same form: (Starting Value)(Growth Multiplier
The starting value is exactly what it sounds, the amount you start with. In this case, it is .
The growth multiplier is how much the value increases each time it changes. In this case, we can get the growth multiplier/factor
from the phrase “”.
The number of cycles is a bit more tricky - you know that the growth factor is applied every , and you want to know the result
after . Use these pieces of information to get how many times the value is multiplied - i.e. the number of growth
cycles.
You are studying a which you know . If you have a container with of your , how much of the would you have after ? (Note
you don’t need to fully calculate the value, just enter the calculation without simplifying)
Theoretically Harder Difficulty Problem
Remember, all exponential growth/decay problems have the same form: (Starting Value)(Growth Multiplier
The starting value is exactly what it sounds, the amount you start with. In this case, it is .
The growth multiplier is trickier in this case - because financial terminology gets in the way. To find the growth factor/multiplier,
you need to determine how much interest is applied each time it is applied. You can figure this out by taking the annual interest
(in this case and divide it by the number of times it is compounded each year.
Remember to convert the annual interest rate into decimal format, so you would divide by to get the decimal, then divide the
result by the number of times it would be compounded in a year (which you can determine from the ’compounded
’).
Also remember that the number calculated in the last hint is how much interest is added - but it doesn’t include the fact that the
entire principle stays each time too, so you need to add 1 to the number from the last hint to get your growth
factor/multiplier.
To get the number of cycles, you need to know how many times the interest is compounded over the time period it asks about,
i.e. how many times interest is compounded () over years.
For a holiday you receive a bond from a family member. The bond has an initial investment of $ and earns % per year,
compounded . The bond accrues interest for years, at which point it is deposited in your checking account. How much
will be deposited into your checking account? (Note that you don’t need to compute the answer, just set up the
calculation)
$
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Start typing the name of a mathematical function to automatically insert it.
(For example, "sqrt" for root, "mat" for matrix, or "defi" for definite integral.)