Exponential growth and decay

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•
Mathematics
•
12th Grade
•
Hard
Standards-aligned
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15 questions
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1.
FLASHCARD QUESTION
Front
What is exponential growth?
Back
Exponential growth occurs when the growth rate of a value is proportional to its current value, leading to growth that accelerates over time. It can be modeled by the equation f(t) = a(1 + r)^t, where 'a' is the initial amount, 'r' is the growth rate, and 't' is time.
Tags
CCSS.HSF-LE.A.1A
2.
FLASHCARD QUESTION
Front
What is exponential decay?
Back
Exponential decay is the process of reducing an amount by a consistent percentage rate over a period of time. It can be modeled by the equation f(t) = a(1 - r)^t, where 'a' is the initial amount, 'r' is the decay rate, and 't' is time.
Tags
CCSS.HSF-IF.C.8B
3.
FLASHCARD QUESTION
Front
What does the variable 'a' represent in the exponential function f(t) = a(1 + r)^t?
Back
'a' represents the initial amount or starting value before any growth or decay occurs.
Tags
CCSS.HSF-IF.C.8B
4.
FLASHCARD QUESTION
Front
What does the variable 'r' represent in the exponential function?
Back
'r' represents the growth or decay rate expressed as a decimal.
Tags
CCSS.HSF-IF.C.8B
5.
FLASHCARD QUESTION
Front
How do you determine if a function models growth or decay?
Back
If the growth factor (1 + r) is greater than 1, the function models growth. If the decay factor (1 - r) is less than 1, the function models decay.
Tags
CCSS.HSF-IF.C.8B
6.
FLASHCARD QUESTION
Front
What is the formula for compound interest?
Back
The formula for compound interest is A = P(1 + r/n)^(nt), where A is the amount of money accumulated after n years, P is the principal amount (the initial amount of money), r is the annual interest rate (decimal), n is the number of times that interest is compounded per year, and t is the number of years.
7.
FLASHCARD QUESTION
Front
Calculate the total amount after 2 years for $2750 at 8% interest compounded annually.
Back
Using the formula A = P(1 + r/n)^(nt), we have A = 2750(1 + 0.08/1)^(1*2) = 2750(1.08)^2 = 2750 * 1.1664 = $3207.60.
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