Writing Exponential Functions for Word Problems
Flashcard
•
Mathematics
•
9th - 12th Grade
•
Practice Problem
•
Hard
+2
Standards-aligned
Wayground Content
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15 questions
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1.
FLASHCARD QUESTION
Front
What is an exponential function?
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. It represents growth or decay processes.
2.
FLASHCARD QUESTION
Front
How do you write an exponential function for a situation where a quantity doubles over time?
Back
If a quantity doubles every hour, the exponential function can be written as f(t) = a(2^t), where 'a' is the initial amount and 't' is the time in hours.
Tags
CCSS.HSF.LE.A.2
3.
FLASHCARD QUESTION
Front
What does it mean for a value to depreciate at a certain percentage per year?
Back
Depreciation at a certain percentage means that the value decreases by that percentage each year. The exponential function for depreciation can be modeled as y = initial_value * (1 - rate)^t.
4.
FLASHCARD QUESTION
Front
How do you calculate the future value of an investment that grows at a constant percentage rate?
Back
The future value can be calculated using the formula: Future Value = Present Value * (1 + growth_rate)^t, where 't' is the number of time periods.
Tags
CCSS.HSF.BF.A.2
5.
FLASHCARD QUESTION
Front
What is the formula for calculating population growth?
Back
The formula for population growth is P(t) = P0 * (1 + r)^t, where P0 is the initial population, r is the growth rate, and t is the time in years.
6.
FLASHCARD QUESTION
Front
If a cell phone store sells 417 phones and sales increase by 3.75% per month, how is this modeled?
Back
The sales can be modeled by the function f(x) = 417(1.0375)^x, where x is the number of months after January.
Tags
CCSS.HSF-LE.A.1C
7.
FLASHCARD QUESTION
Front
What is the difference between growth and decay in exponential functions?
Back
Growth occurs when the base of the exponential function is greater than 1 (e.g., f(x) = a(b^x) with b > 1), while decay occurs when the base is between 0 and 1 (e.g., f(x) = a(b^x) with 0 < b < 1).
Tags
CCSS.HSF-IF.C.8B
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