How do you convert a word problem into an exponential equation?

Translate the problem into mathematical terms, identifying the initial amount and the growth/decay factor, then use the form $$y = a \times b^x$$ .

What does the variable $$x$$ represent in an exponential function?

In an exponential function, $$x$$ typically represents time or the number of intervals over which growth or decay occurs.

What is the difference between exponential growth and linear growth?

Exponential growth increases at a rate proportional to its current value, while linear growth increases by a constant amount.

How can you determine if a function is exponential from its graph?

A graph of an exponential function will show a curve that rises or falls sharply, rather than a straight line.

What is the formula for exponential growth?

The formula for exponential growth is $$y = a \times (1 + r)^t$$ , where $$r$$ is the growth rate and $$t$$ is time.

What is the formula for exponential decay?

The formula for exponential decay is $$y = a \times (1 - r)^t$$ , where $$r$$ is the decay rate and $$t$$ is time.

How do you find the equation of an exponential function given a graph?

Identify key points on the graph, determine the initial value and the growth/decay factor, and use the form $$y = a \times b^x$$ .

What is the role of the exponent in an exponential function?

The exponent determines how many times the base is multiplied by itself, affecting the rate of growth or decay.

Writing Exponential Functions Flashcards

Student preview

15 questions

Show all answers

1.

FLASHCARD QUESTION

Front

What is an exponential function?

Back

2.

FLASHCARD QUESTION

Front

What does the base of an exponential function represent?

Back

Tags

CCSS.HSF-IF.C.8B

3.

FLASHCARD QUESTION

Front

How do you identify an exponential function from a table of values?

Back

An exponential function can be identified if the ratio of consecutive outputs (y-values) is constant when the inputs (x-values) are increased by equal intervals.

Tags

CCSS.HSF-LE.A.1A

4.

FLASHCARD QUESTION

Front

What is the general form of an exponential growth function?

Back

5.

FLASHCARD QUESTION

Front

What is the general form of an exponential decay function?

Back

6.

FLASHCARD QUESTION

Front

How do you write an exponential function from a word problem?

Back

Tags

CCSS.HSF.LE.A.2

7.

FLASHCARD QUESTION

Front

What is the significance of the initial value in an exponential function?

Back

Tags

CCSS.HSF-IF.C.8B

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