How do you determine the amount remaining after a certain time in exponential decay?

To determine the amount remaining, use the formula $$A = A_0 \times (1 - r)^t$$ , where $$A_0$$ is the initial amount, 'r' is the decay rate, and 't' is the time.

What is the relationship between the initial value and the decay factor in exponential decay?

The initial value is multiplied by the decay factor raised to the power of time to find the remaining amount: $$A = A_0 \times (decay\factor)^t$$ .

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

The base determines the rate of growth or decay. If the base is greater than 1, the function represents growth; if it is between 0 and 1, it represents decay.

How can you identify the initial value from an equation like $$y = 6.87(4)^x$$ ?

The initial value is the coefficient of the function when $$x = 0$$ , which is $$6.87$$ in this case.

What does it mean if a population grows at a rate of 25% per month?

It means that each month, the population increases by 25% of its current size, leading to exponential growth.

How do you write an equation for a quantity that decays by 8% per year?

The equation can be written as $$y = A_0 \times (0.92)^t$$ , where $$A_0$$ is the initial amount and $$0.92$$ is the decay factor.

What is the formula to calculate the remaining amount after multiple time periods in exponential decay?

The formula is $$A = A_0 \times (decay\factor)^t$$ , where 't' is the number of time periods.

How do you find the decay factor from a percentage decay rate?

To find the decay factor, subtract the decay rate from 1: $$decay\factor = 1 - r$$ , where 'r' is the decay rate expressed as a decimal.

Skills Check 5.1a: Using Exponential Functions Flashcards

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1.

FLASHCARD QUESTION

Front

What is an exponential function?

Back

2.

FLASHCARD QUESTION

Front

What does the decay factor represent in exponential decay?

Back

3.

FLASHCARD QUESTION

Front

If a quantity decreases by 20% per hour, what is the decay factor?

Back

4.

FLASHCARD QUESTION

Front

What is the initial value in an exponential function?

Back

5.

FLASHCARD QUESTION

Front

How do you write an equation for exponential growth?

Back

6.

FLASHCARD QUESTION

Front

What is the formula for exponential decay?

Back

7.

FLASHCARD QUESTION

Front

What does a 25% growth rate mean in terms of the growth factor?

Back

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