Warm-Up_Exponential Growth and Decay

Front

What is exponential growth?

Back

Exponential growth occurs when the increase of a quantity is proportional to its current value, leading to growth at a constant percentage rate over time.

Front

What is exponential decay?

Back

Exponential decay describes the process of reducing an amount by a consistent percentage rate over a period of time, often seen in radioactive decay.

Front

Define half-life.

Back

Half-life is the time required for a quantity to reduce to half its initial amount, commonly used in the context of radioactive substances.

Front

What is the formula for exponential growth?

Back

The formula for exponential growth is f(t) = a(1 + r)^t, where 'a' is the initial amount, 'r' is the growth rate, and 't' is time.

Front

What is the formula for exponential decay?

Back

The formula for exponential decay is f(t) = a(1 - r)^t, where 'a' is the initial amount, 'r' is the decay rate, and 't' is time.

Front

How do you calculate the remaining amount after one half-life?

Back

To calculate the remaining amount after one half-life, divide the initial amount by 2.

Front

If a substance has a half-life of 10 years, how much of a 100g sample remains after 20 years?

Back

After 20 years (2 half-lives), 25g of the sample remains.

Front

What is the growth factor in the function f(x) = 417(1.0375)^x?

Back

The growth factor is 1.0375, indicating a 3.75% increase per month.

Front

How do you determine the number of half-lives that have passed?

Back

To determine the number of half-lives, divide the total time elapsed by the half-life duration.

Front

What is the remaining amount of a substance after 3 half-lives if the initial amount is 80g?

Back

After 3 half-lives, 10g of the substance remains.