What is the initial value in an exponential function?

The initial value is the value of the function when $$x = 0$$ . In the function $$f(x) = 6(1.14)^x$$ , the initial value is 6.

How do you determine the value of an exponential function at a specific point?

To determine the value of an exponential function at a specific point, substitute the value of $$x$$ into the function and calculate. For example, for $$f(x) = 3(2)^x$$ at $$x = 2$$ , calculate $$f(2) = 3(2)^2 = 12$$ .

What does it mean if an exponential function has a base greater than 1?

If an exponential function has a base greater than 1, it indicates exponential growth. For example, in $$f(x) = 5(3)^x$$ , the population or value increases as $$x$$ increases.

What is the general form of an exponential decay function?

The general form of an exponential decay function is $$f(x) = a(1 - r)^x$$ , where $$a$$ is the initial amount and $$r$$ is the decay rate.

How do you find the half-life in exponential decay?

The half-life is the time it takes for a quantity to reduce to half its initial value. It can be calculated using the formula $$t_{1/2} = \frac{\text{ln}(0.5)}{\text{ln}(b)}$$ , where $$b$$ is the base of the decay function.

What is the significance of the constant 'a' in an exponential function?

The constant 'a' represents the initial value or starting amount of the function before any growth or decay occurs.

How can you graph an exponential function?

To graph an exponential function, plot points by substituting values for $$x$$ into the function, then connect the points to show the curve, which will rise or fall steeply depending on the base.

What is the relationship between exponential functions and logarithms?

Exponential functions and logarithms are inverse functions. The logarithm of a number is the exponent to which the base must be raised to produce that number.

Exponential Functions EOC Review Flashcards

Student preview

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

3.

FLASHCARD QUESTION

Front

How do you identify exponential decay in a function?

Back

4.

FLASHCARD QUESTION

Front

What is the decay rate in an exponential function?

Back

5.

FLASHCARD QUESTION

Front

Write the equation for a population decreasing by 6% per year starting at 10,000.

Back

6.

FLASHCARD QUESTION

Front

What is the formula for exponential growth?

Back

7.

FLASHCARD QUESTION

Front

How do you convert a percentage growth rate to a decimal for an exponential function?

Back

To convert a percentage growth rate to a decimal, divide by 100. For example, a growth rate of 14% becomes 0.14.

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