exponential growth and decay

Front

What is exponential growth?

Back

Exponential growth occurs when a quantity increases by a consistent percentage over a period of time, leading to rapid increases as time goes on.

Front

What is exponential decay?

Back

Exponential decay occurs when a quantity decreases by a consistent percentage over a period of time, leading to rapid decreases as time goes on.

Front

What is the formula for exponential growth?

Back

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

Front

What is the formula for exponential decay?

Back

The formula is: 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 1,000 increases by 10% each year, what will it be after 3 years?

Back

y = 1000(1.10)^3 = 1331.

Front

If a substance decays from 200 grams at a rate of 20% per hour, how much will remain after 2 hours?

Back

y = 200(0.80)^2 = 128 grams.

Front

What does the term 'initial value' mean in exponential functions?

Back

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

Front

How do you identify exponential growth from a graph?

Back

Exponential growth graphs curve upwards, showing a steep increase as time progresses.

Front

How do you identify exponential decay from a graph?

Back

Exponential decay graphs curve downwards, showing a steep decrease as time progresses.

Front

What is the significance of the base in an exponential function?

Back

The base indicates the growth or decay factor; a base greater than 1 indicates growth, while a base between 0 and 1 indicates decay.