What is the formula for exponential decay?

The formula for exponential decay is given by $$f(t) = a \times e^{-kt}$$ , where 'a' is the initial amount, 'k' is the decay constant, and 't' is time.

Explain the concept of doubling time in exponential growth.

Doubling time is the period it takes for a quantity to double in size or value. It can be calculated using the rule of 70: $$T_d = \frac{70}{r}$$ , where 'r' is the growth rate.

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

The base in an exponential function determines the rate of growth or decay. A base greater than 1 indicates growth, while a base between 0 and 1 indicates decay.

How do you find the value of a truck after a certain number of years using exponential decay?

To find the value of a truck after a certain number of years, use the formula $$V(t) = V_0 \times (0.85)^{t}$$ , where $$V_0$$ is the initial value and $$t$$ is the number of years.

What is the relationship between exponential functions and logarithms?

Exponential functions and logarithms are inverse operations. If $$y = b^x$$ , then $$x = \text{log}_b(y)$$ .

How do you express a population growth model mathematically?

A population growth model can be expressed as $$P(t) = P_0 \times e^{rt}$$ , where $$P_0$$ is the initial population, $$r$$ is the growth rate, and $$t$$ is time.

What is the formula for calculating the amount of medication left after a certain time?

The formula for calculating the amount of medication left after time 'h' is $$f(h) = A_0 \times (0.5)^{\frac{h}{T_{1/2}}}$$ , where $$A_0$$ is the initial amount and $$T_{1/2}$$ is the half-life.

IM Algebra 2 - Unit 4 Mid Review Flashcards

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FLASHCARD QUESTION

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What is an exponential function?

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FLASHCARD QUESTION

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Define the decay factor in exponential decay.

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