Exponential Growth and Decay Functions

Flashcard
•
Mathematics
•
11th Grade
•
Hard
+2
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1.
FLASHCARD QUESTION
Front
What is an exponential growth function?
Back
An exponential growth function is a mathematical expression of the form y = a(1 + r)^t, where 'a' is the initial amount, 'r' is the growth rate, and 't' is time. It describes a situation where the quantity increases at a rate proportional to its current value.
Tags
CCSS.HSF-IF.C.8B
2.
FLASHCARD QUESTION
Front
What is an exponential decay function?
Back
An exponential decay function is a mathematical expression of the form y = a(1 - r)^t, where 'a' is the initial amount, 'r' is the decay rate, and 't' is time. It describes a situation where the quantity decreases at a rate proportional to its current value.
Tags
CCSS.HSF-IF.C.8B
3.
FLASHCARD QUESTION
Front
What does the horizontal asymptote of an exponential function represent?
Back
The horizontal asymptote of an exponential function represents the value that the function approaches as x approaches infinity. For exponential growth, this is typically the x-axis (y=0).
Tags
CCSS.HSF-IF.C.7E
4.
FLASHCARD QUESTION
Front
How do you calculate compound interest?
Back
Compound interest can be calculated using the formula A = P(1 + r/n)^(nt), where A is the amount of money accumulated after n years, P is the principal amount, r is the annual interest rate, n is the number of times that interest is compounded per year, and t is the number of years.
5.
FLASHCARD QUESTION
Front
What is the formula for continuous growth?
Back
The formula for continuous growth is A = Pe^(rt), where A is the amount after time t, P is the initial amount, r is the growth rate, and e is the base of the natural logarithm.
6.
FLASHCARD QUESTION
Front
What is the significance of the initial amount in exponential functions?
Back
The initial amount in exponential functions represents the starting value before any growth or decay occurs. It is the value of the function when time (t) is zero.
Tags
CCSS.HSF.LE.B.5
7.
FLASHCARD QUESTION
Front
How do you determine the growth rate from an exponential function?
Back
The growth rate can be determined from an exponential function of the form y = a(1 + r)^t by rearranging the equation to solve for r, where r = (y/a)^(1/t) - 1.
Tags
CCSS.HSF-IF.C.8B
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