Exponential Growth and Decay Percent Problems

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 does the base of an exponential function represent in growth problems?

Back

In growth problems, the base represents the growth factor, which is greater than 1.

Front

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

Back

In decay problems, the base represents the decay factor, which is less than 1.

Front

How do you write an exponential decay function?

Back

An exponential decay function can be written as y = a(1 - r)^t, where a is the initial amount, r is the decay rate, and t is time.

Front

How do you write an exponential growth function?

Back

An exponential growth function can be written as y = a(1 + r)^t, where a is the initial amount, r is the growth rate, and t is time.

Front

What does the initial value in an exponential function represent?

Back

The initial value represents the starting amount before any growth or decay occurs.

Front

If a population decreases by 20% each year, what is the decay factor?

Back

The decay factor is 0.8, calculated as 1 - 0.20.

Front

What is the formula to find the remaining amount after a percentage fee is applied?

Back

The formula is y = a(1 - r)^t, where a is the initial amount, r is the fee percentage, and t is time.

Front

How do you determine the percentage decrease from an initial value?

Back

Percentage decrease can be calculated using the formula: (initial value - final value) / initial value * 100%.