What does the term 'exponential growth' mean?

Exponential growth refers to an increase in quantity where the rate of growth is proportional to the current amount, leading to rapid increases over time.

What does the term 'exponential decay' mean?

Exponential decay refers to a decrease in quantity where the rate of decay is proportional to the current amount, leading to rapid decreases over time.

What is the y-intercept of the function $$f(x) = 2 \times 4^x$$ ?

The y-intercept is 2, which is the value of the function when x = 0.

If a function is modeled by $$B(t) = 1850(0.75)^t$$ , what does 0.75 indicate?

0.75 indicates that the bacteria population decreases to 75% of its previous amount each minute.

What is the formula for finding the value of an exponential function at a specific point?

To find the value of an exponential function at a specific point, substitute the value of x into the function: $$f(x) = a \times b^x$$ .

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

The base determines the rate of growth or decay; a base greater than 1 indicates growth, while a base between 0 and 1 indicates decay.

How can you determine if a function is exponential from a table of values?

If the ratio of consecutive outputs is constant, the function is exponential.

What is the relationship between exponential functions and their graphs?

The graph of an exponential function is a smooth curve that either rises steeply (growth) or falls steeply (decay) as x increases.

Exponential Functions and Their Characteristics 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 does the 'a' represent in an exponential function?

Back

'a' represents the initial value or the y-intercept of the function.

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