What is the formula for calculating the amount remaining after exponential decay?

The formula is: $$y = a e^{-kt}$$ , where 'a' is the initial amount, 'k' is the decay constant, and 't' is time.

How do you convert a percentage decay rate to a decimal for calculations?

To convert a percentage decay rate to a decimal, divide by 100. For example, a 25% decay rate becomes 0.25.

What is the formula for continuous exponential growth?

The formula for continuous exponential growth is: $$y = ae^{rt}$$ , where 'a' is the initial amount, 'r' is the growth rate, and 't' is time.

If a substance has a half-life of 4 hours, how much of a 100 mg sample remains after 12 hours?

After 12 hours, 12/4 = 3 half-lives have passed. Remaining amount: $$100(0.5)^3 = 12.5 mg$$ .

What is the difference between exponential growth and linear growth?

Exponential growth increases at a rate proportional to its current value, while linear growth increases by a constant amount.

How do you find the decay constant 'k' from a decay rate?

The decay constant 'k' can be found using the formula: $$k = -\frac{\text{ln}(1 - r)}{t}$$ , where 'r' is the decay rate and 't' is time.

What is the significance of the number 'e' in exponential functions?

The number 'e' (approximately 2.718) is the base of natural logarithms and is used in continuous growth and decay models.

How can you model a situation where a quantity decreases by a fixed percentage each year?

You can model it using the formula: $$y = a(1 - r)^t$$ , where 'r' is the fixed percentage expressed as a decimal.

Resource Library

Math

Algebra

Exponential Growth And Decay

Exponential Growth And Decay Problems

Exponential Growth and Decay Problems

Flashcard

•

Mathematics

•

12th Grade

•

Practice Problem

•

Hard

•

CCSS

HSF-LE.A.1A, HSF-IF.C.8B, HSF.LE.B.5

Standards-aligned

Wayground Content

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15 questions

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FLASHCARD QUESTION

Front

What is the formula for exponential decay?

Back

Tags

CCSS.HSF-LE.A.1A

FLASHCARD QUESTION

Front

Define half-life in the context of exponential decay.

Back

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

FLASHCARD QUESTION

Front

What is the initial value in the function f(t) = 200(0.9)^t?

Back

The initial value is 200.

Tags

CCSS.HSF.LE.B.5

FLASHCARD QUESTION

Front

Write the exponential growth equation for an initial amount of 100 with a growth rate of 20% per year.

Back

Tags

CCSS.HSF-LE.A.1A

FLASHCARD QUESTION

Front

How do you determine the remaining amount after a certain time using the half-life concept?

Back

FLASHCARD QUESTION

Front

What does the base of an exponential function represent in growth and decay?

Back

In growth, the base is greater than 1, indicating an increase. In decay, the base is between 0 and 1, indicating a decrease.

Tags

CCSS.HSF-IF.C.8B

FLASHCARD QUESTION

Front

If a population of bacteria doubles every 3 hours, what is the growth factor?

Back

The growth factor is 2, as the population doubles.

Tags

CCSS.HSF-LE.A.1A

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