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 process where a quantity decreases at a rate proportional to its current value, resulting in a rapid decrease that slows over time.

Front

In the function y = a(1 + r)^x, what does 'a' represent?

Back

'a' represents the initial value or starting amount before growth or decay occurs.

Front

In the function y = a(1 + r)^x, what does 'r' represent?

Back

'r' represents the rate of growth (if positive) or decay (if negative) expressed as a decimal.

Front

How do you convert a percentage rate to a decimal for calculations?

Back

To convert a percentage to a decimal, divide the percentage by 100. For example, 30% becomes 0.30.

Front

What is the formula for exponential decay?

Back

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

Front

If a population of 1000 decreases by 20% each year, what is the equation representing this situation?

Back

y = 1000(1 - 0.20)^x.

Front

What is the value of 'r' in the function y = 5(1.05)^x?

Back

'r' is 0.05, which represents a 5% growth rate.

Front

If a culture of bacteria starts with 5000 cells and dies by 30% each year, what is the starting value?

Back

The starting value is 5000.

Front

What is the population of fish after 10 years if it starts at 8000 and decreases by 6% per year?

Back

The population after 10 years is approximately 4309 fish.