Exponential Functions - WORD PROBLEMS

Front

What is an exponential function?

Back

An exponential function is a mathematical function of the form y = a(b^x), where 'a' is a constant, 'b' is the base (a positive real number), and 'x' is the exponent. It shows rapid growth or decay.

Front

What does exponential growth mean?

Back

Exponential growth occurs when a quantity increases by a fixed percentage over a period of time, resulting in a rapid increase.

Front

What does exponential decay mean?

Back

Exponential decay occurs when a quantity decreases by a fixed percentage over a period of time, leading to a rapid decrease.

Front

How do you identify exponential growth on a graph?

Back

Exponential growth is identified by a curve that rises steeply as it moves from left to right.

Front

How do you identify exponential decay on a graph?

Back

Exponential decay is identified by a curve that falls steeply as it moves from left to right.

Front

What is the formula for exponential growth?

Back

The formula for exponential growth 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 for exponential decay 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 bacteria doubles every hour, what type of function does this represent?

Back

This represents exponential growth.

Front

What is the initial value in an exponential decay problem?

Back

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

Front

How do you write an exponential decay equation for a value that decreases by 20% each year?

Back

The equation would be y = a(0.8)^t, where 'a' is the initial amount.