Modeling 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 an increasing rate over time.

Front

What is exponential decay?

Back

Exponential decay is the decrease of a quantity at a rate proportional to its current value, resulting in a rapid decline that slows over time.

Front

What is the general formula for exponential growth?

Back

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

Front

What is the general formula for exponential decay?

Back

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

Front

How do you identify a linear function?

Back

A linear function has a constant rate of change and can be represented by the equation y = mx + b.

Front

How do you identify an exponential function?

Back

An exponential function has a variable in the exponent and can be represented by the form y = ab^x.

Front

What does the base in an exponential function represent?

Back

The base indicates the growth or decay factor; if the base is greater than 1, it represents growth, and if it is between 0 and 1, it represents decay.

Front

What is the growth rate in the equation y = 5(1.27)^x?

Back

The growth rate is 27%.

Front

What is the decay rate in the equation A = 1200(0.85)^6?

Back

The decay rate is 0.15 or 15%.

Front

How do you write an equation for a population that decreases by a certain percentage each year?

Back

Use the formula y = a(1 - r)^x, where 'a' is the initial population and 'r' is the decay rate.