What is the y-intercept of the function $$f(x) = 3(2)^x$$ ?

The y-intercept is 3, which means that when $$x = 0$$ , $$f(0) = 3(2)^0 = 3$$ .

What is the general form of an exponential decay function?

The general form is $$f(x) = a \times b^x$$ , where $$0

If $$f(x) = 25(0.20)^x$$ , what type of function is this?

This is an example of exponential decay because the base 0.20 is less than 1.

If $$f(x) = 0.25(1.3)^x$$ , what type of function is this?

This is an example of exponential growth because the base 1.3 is greater than 1.

What does the term 'exponential growth' imply in real-world scenarios?

Exponential growth implies that a quantity increases rapidly over time, often seen in populations or investments.

What does the term 'exponential decay' imply in real-world scenarios?

Exponential decay implies that a quantity decreases rapidly over time, often seen in radioactive decay or depreciation.

How do you find the initial value in an exponential function?

The initial value can be found by evaluating the function at $$x = 0$$ , which gives $$f(0) = a$$ .

What is the significance of the base in an exponential function?

The base determines the rate of growth or decay; a larger base results in faster growth, while a smaller base (but greater than 0) results in faster decay.

How can you graph an exponential function?

To graph an exponential function, plot points for various values of $$x$$ , starting with the y-intercept, and observe the rapid increase or decrease as $$x$$ changes.

Exponential Functions Flashcards

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15 questions

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1.

FLASHCARD QUESTION

Front

What is an exponential function?

Back

2.

FLASHCARD QUESTION

Front

What is the difference between exponential growth and exponential decay?

Back

3.

FLASHCARD QUESTION

Front

What does the constant 'a' represent in an exponential function?

Back

4.

FLASHCARD QUESTION

Front

How can you identify exponential growth from a function?

Back

5.

FLASHCARD QUESTION

Front

How can you identify exponential decay from a function?

Back

6.

FLASHCARD QUESTION

Front

Back

7.

FLASHCARD QUESTION

Front

What does it mean if the base of an exponential function is less than 1?

Back

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