What is an exponential function?
Writing Exponential Functions (Word Problems)

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Mathematics
•
9th Grade
•
Hard
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1.
FLASHCARD QUESTION
Front
Back
An exponential function is a mathematical function of the form f(x) = a(b)^x, where 'a' is a constant, 'b' is the base (a positive real number), and 'x' is the exponent.
2.
FLASHCARD QUESTION
Front
What does the base of an exponential function represent?
Back
The base of an exponential function indicates the growth (if greater than 1) or decay (if between 0 and 1) rate of the function.
3.
FLASHCARD QUESTION
Front
How do you determine the growth rate from an exponential function?
Back
The growth rate can be determined by subtracting 1 from the base of the function. For example, in f(x) = a(1 + r)^x, r is the growth rate.
4.
FLASHCARD QUESTION
Front
What is the decay rate in the function f(x) = 800(0.85)^x?
Back
The decay rate is 15%, which is calculated as 1 - 0.85.
5.
FLASHCARD QUESTION
Front
How do you write an exponential function for a situation involving growth?
Back
To write an exponential function for growth, use the formula C(t) = C_0(1 + r)^t, where C_0 is the initial amount, r is the growth rate, and t is time.
6.
FLASHCARD QUESTION
Front
What is the formula to calculate the future value of an investment with exponential growth?
Back
The future value can be calculated using the formula A = P(1 + r)^t, where A is the amount of money accumulated after n years, P is the principal amount, r is the annual interest rate, and t is the number of years.
7.
FLASHCARD QUESTION
Front
What is the decay factor in the function f(x) = 15000(0.92)^x?
Back
The decay factor is 0.92, which represents the percentage of the value retained after each time period.
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