If a population of 1000 decreases by 10% each year, what is the equation representing this decay?

The equation is $$y = 1000(1 - 0.10)^t$$ .

What is the half-life in the context of exponential decay?

Half-life is the time required for a quantity to reduce to half its initial value, commonly used in radioactive decay.

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

You can use the equation $$y = a(1 - r)^t$$ and solve for 't' by rearranging the equation.

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.

In the equation $$y = 205(0.25)^t$$ , what does 205 represent?

205 represents the initial value or starting amount before any decay occurs.

If a car's value is $20,000 and it depreciates by 15% each year, what is the equation for its value over time?

The equation is $$y = 20000(1 - 0.15)^t$$ .

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 graph an exponential function?

To graph an exponential function, plot points for various values of 't' using the equation, and connect them to show the curve, which will rise steeply for growth or fall steeply for decay.

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 or starting amount of the quantity before any growth or decay occurs.

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 the future value of an investment with exponential growth?

Back

7.

FLASHCARD QUESTION

Front

What is the formula to calculate the future value of an investment with exponential decay?

Back

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