If a population of 1000 decreases by 5% each year, what is the population after 3 years?

Using the formula $$P = 1000(1 - 0.05)^3$$ , the population after 3 years is approximately 857.

What is the difference between linear and exponential functions?

Linear functions increase or decrease by a constant amount, while exponential functions increase or decrease by a constant percentage. Linear functions have the form $$y = mx + b$$ , while exponential functions have the form $$y = ab^x$$ .

What is the growth factor in an exponential growth equation?

The growth factor is the base of the exponent in the equation. For example, in $$y = 21(1.13)^x$$ , the growth factor is 1.13.

What is the decay factor in an exponential decay equation?

The decay factor is the base of the exponent in the equation. For example, in $$y = 100(0.85)^x$$ , the decay factor is 0.85.

How do you find the time it takes for a quantity to reach a certain value in exponential decay?

You can use the formula $$t = \frac{\text{ln}(A/P)}{\text{ln}(1 - r)}$$ , where 'A' is the final amount, 'P' is the initial amount, and 'r' is the decay rate.

What is a real-world example of exponential growth?

A common example is population growth, where a population increases at a constant percentage rate, such as bacteria doubling in number every hour.

What is a real-world example of exponential decay?

A common example is radioactive decay, where a substance decreases in quantity at a constant percentage rate over time.

How can you graph an exponential function?

To graph an exponential function, plot points for various values of 'x' and connect them smoothly. The graph will show rapid increases (growth) or decreases (decay) depending on the base of the exponent.

Exponential Growth and Decay Review Flashcards

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15 questions

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1.

FLASHCARD QUESTION

Front

What is exponential growth?

Back

2.

FLASHCARD QUESTION

Front

What is exponential decay?

Back

3.

FLASHCARD QUESTION

Front

What does the y-intercept represent in an exponential function?

Back

The y-intercept represents the initial value of the quantity before any growth or decay occurs. It is the value of 'y' when 'x' is 0.

4.

FLASHCARD QUESTION

Front

How do you identify exponential growth from an equation?

Back

5.

FLASHCARD QUESTION

Front

How do you identify exponential decay from an equation?

Back

6.

FLASHCARD QUESTION

Front

What is the formula to calculate future value in exponential growth?

Back

7.

FLASHCARD QUESTION

Front

What is the formula to calculate future value in exponential decay?

Back

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