Exponential Growth and Decay Review

Front

What is exponential growth?

Back

Exponential growth occurs when a quantity increases by a consistent percentage over a period of time, resulting in a rapid increase. For example, if a population grows by 20% each year, it will grow faster each subsequent year.

Front

What is exponential decay?

Back

Exponential decay occurs when a quantity decreases by a consistent percentage over time, leading to a rapid decrease. For example, if a population decreases by 10% each year, it will decline faster each subsequent year.

Front

What is the general formula for exponential growth?

Back

The general formula for exponential growth is y = a(1 + r)^x, where 'a' is the initial amount, 'r' is the growth rate, and 'x' is the time.

Front

What is the general formula for exponential decay?

Back

The general formula for exponential decay is y = a(1 - r)^x, where 'a' is the initial amount, 'r' is the decay rate, and 'x' is the time.

Front

In the equation y = 530(1 - 0.04)^x, what does 0.04 represent?

Back

In this equation, 0.04 represents the decay rate of 4% per year.

Front

How do you determine the y-intercept in an exponential equation?

Back

The y-intercept in an exponential equation of the form y = a(b)^x is the value of 'a', which represents the initial amount when x = 0.

Front

If a population of 1000 is decreasing by 5% each year, what will the population be after 3 years?

Back

The population after 3 years will be approximately 857.66, calculated using the formula: y = 1000(1 - 0.05)^3.

Front

What does it mean if an equation has a base greater than 1?

Back

If an equation has a base greater than 1, it indicates exponential growth.

Front

What does it mean if an equation has a base between 0 and 1?

Back

If an equation has a base between 0 and 1, it indicates exponential decay.

Front

In the context of depreciation, what does a 10% annual depreciation mean?

Back

A 10% annual depreciation means that the value of an asset decreases by 10% of its current value each year.