Flashcard - Exponential Growth and Decay

Front

What is exponential growth?

Back

Exponential growth occurs when the increase in a quantity is proportional to its current value, leading to growth at an increasing rate. For example, if a population grows by 20% each year, it grows faster each year as the base population increases.

Front

What is exponential decay?

Back

Exponential decay is the process of reducing an amount by a consistent percentage rate over a period of time. For example, if a substance decays at a rate of 10% per year, it loses 10% of its current amount each year.

Front

Write the general formula for exponential growth.

Back

y = a(1 + r)^t, where 'a' is the initial amount, 'r' is the growth rate, and 't' is time.

Front

Write the general formula for exponential decay.

Back

y = a(1 - r)^t, where 'a' is the initial amount, 'r' is the decay rate, and 't' is time.

Front

If a population of 1000 increases by 50% each year, what will be the population after 2 years?

Back

y = 1000(1.5)^2 = 2250.

Front

If a culture of bacteria starts with 2000 cells and dies by 20% each year, what is the equation representing this situation?

Back

y = 2000(0.8)^t.

Front

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

Back

In growth situations, the base (greater than 1) represents the growth factor, indicating how much the quantity increases each time period.

Front

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

Back

In decay situations, the base (between 0 and 1) represents the decay factor, indicating how much the quantity decreases each time period.

Front

How do you determine if a function represents exponential growth or decay?

Back

If the base of the exponential function is greater than 1, it represents growth. If the base is between 0 and 1, it represents decay.

Front

What is the effect of a higher growth rate on exponential growth?

Back

A higher growth rate leads to a faster increase in the quantity, resulting in a steeper growth curve.