Exponential Modeling

Flashcard
•
Mathematics
•
9th - 12th Grade
•
Hard
+1
Standards-aligned
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15 questions
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1.
FLASHCARD QUESTION
Front
What is exponential modeling?
Back
Exponential modeling is a mathematical technique used to describe situations where a quantity grows or decays at a rate proportional to its current value, often represented by the function y = a(1 + r)^t, where 'a' is the initial amount, 'r' is the growth rate, and 't' is time.
2.
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 investment), 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 the money is invested or borrowed.
3.
FLASHCARD QUESTION
Front
How do you calculate the future value of an investment compounded quarterly?
Back
To calculate the future value of an investment compounded quarterly, use the formula A = P(1 + r/4)^(4t), where P is the principal, r is the annual interest rate, and t is the number of years.
4.
FLASHCARD QUESTION
Front
What does it mean for a population to grow exponentially?
Back
Exponential population growth means that the population increases by a fixed percentage over a specific period, leading to faster growth as the population size increases.
Tags
CCSS.HSF-LE.A.1A
5.
FLASHCARD QUESTION
Front
What is the difference between linear and exponential growth?
Back
Linear growth increases by a constant amount over time, while exponential growth increases by a constant percentage, resulting in a rapid increase as the quantity grows.
6.
FLASHCARD QUESTION
Front
How do you write an exponential growth function?
Back
An exponential growth function can be written in the form y = a(1 + r)^t, where 'a' is the initial value, 'r' is the growth rate, and 't' is time.
7.
FLASHCARD QUESTION
Front
What is the initial value in an exponential function?
Back
The initial value in an exponential function is the starting amount before any growth or decay occurs, represented by 'a' in the function y = a(1 + r)^t.
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