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

The formula is $$A = P(1 + r)^t$$ , where 'A' is the amount of money accumulated after n years, 'P' is the principal amount, 'r' is the annual interest rate (decimal), and 't' is the number of years.

What is the formula to calculate the future value of a depreciating asset?

The formula is $$V = P(1 - r)^t$$ , where 'V' is the value after time 't', 'P' is the initial value, 'r' is the depreciation rate, and 't' is the number of years.

If a population decreases by 6% per year, what is the decay factor?

The decay factor is $$1 - 0.06 = 0.94$$ .

How do you calculate the remaining quantity after multiple periods of decay?

Use the formula $$y = a(1 - r)^t$$ , where 'a' is the initial quantity, 'r' is the decay rate, and 't' is the number of periods.

What is the value of an asset after 8 years if it depreciates at 5% annually from an initial value of $35,000?

The value after 8 years is calculated as $$V = 35000(1 - 0.05)^8$$ , which equals approximately $23,219.72.

What does it mean if a quantity is halved every time period in terms of decay?

It means the decay factor is $$\frac{1}{2}$$ , indicating that the quantity decreases to half its value after each time period.

How can you determine the time it takes for a quantity to decay to a certain level?

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

What is the significance of the initial value in exponential functions?

The initial value represents the starting amount before any growth or decay occurs, serving as the baseline for calculations.

Exponential Growth and Decay 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

Define the decay factor.

Back

4.

FLASHCARD QUESTION

Front

What is the growth factor?

Back

5.

FLASHCARD QUESTION

Front

How do you find the decay factor from a graph?

Back

6.

FLASHCARD QUESTION

Front

Write the exponential decay function for a quantity that decreases by 20% per hour starting from 60 mg.

Back

7.

FLASHCARD QUESTION

Front

Write the exponential growth function for a painting valued at $1400 increasing by 9% per year.

Back

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