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

The initial value (when $$x=0$$ ) represents the starting amount before any growth or decay occurs.

How do you solve for the time in an exponential growth problem?

To solve for time in an exponential growth problem, use the formula $$t = \frac{\text{log}(A/P)}{\text{log}(1 + r)}$$ .

What is the difference between exponential growth and linear growth?

Exponential growth increases by a percentage over time, leading to rapid increases, while linear growth increases by a constant amount.

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

Identify the initial value and the growth/decay factor from the problem, then use the form $$f(x) = a \times b^x$$ to write the function.

What is the formula for continuous exponential growth?

The formula for continuous exponential growth is $$A = Pe^{rt}$$ , where $$e$$ is Euler's number, $$P$$ is the initial amount, $$r$$ is the growth rate, and $$t$$ is time.

How do you graph an exponential function?

To graph an exponential function, plot the y-intercept, identify the growth/decay factor, and draw a curve that reflects the function's behavior.

What is the relationship between exponential functions and logarithms?

Exponential functions and logarithms are inverses of each other. The logarithm can be used to solve for the exponent in an exponential equation.

How do you identify the growth factor in an exponential function?

The growth factor in an exponential function $$f(x) = a \times b^x$$ is the base $$b$$ , which indicates how much the function multiplies by for each unit increase in $$x$$ .

Writing Exponential Functions Flashcard

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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 does the base of an exponential function represent?

Back

Tags

CCSS.HSF-IF.C.8B

3.

FLASHCARD QUESTION

Front

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

Back

Tags

CCSS.HSF.LE.A.2

4.

FLASHCARD QUESTION

Front

What is the general form of an exponential decay function?

Back

Tags

CCSS.HSF-IF.C.8B

5.

FLASHCARD QUESTION

Front

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

Back

A function is exponential if its graph shows a constant percentage rate of change, appearing as a curve that rises or falls sharply.

6.

FLASHCARD QUESTION

Front

What is the formula to calculate the amount after a certain time in exponential growth?

Back

Tags

CCSS.HSF-IF.C.8B

7.

FLASHCARD QUESTION

Front

How do you find the y-intercept of an exponential function?

Back

Tags

CCSS.HSF-IF.C.7E

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