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, resulting in a rapid increase.

Front

What is exponential decay?

Back

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

Front

What does the term 'y-intercept' refer to in a graph?

Back

The y-intercept is the point where the graph intersects the y-axis, representing the initial value of the function when x=0.

Front

How do you calculate the future value of an investment with exponential growth?

Back

Use the formula: Future Value = Present Value * (1 + growth rate)^number of years.

Front

How do you calculate the remaining value of a decaying quantity?

Back

Use the formula: Remaining Value = Initial Value * (decay factor)^number of time periods.

Front

What is the decay factor in the function f(x) = 800(0.87)^x?

Back

The decay factor is 0.87, indicating a 13% decay rate.

Front

If a quantity is decreasing by 20% each year, what is the decay factor?

Back

The decay factor is 0.80.

Front

What is the difference between linear and exponential functions?

Back

Linear functions increase or decrease by a constant amount, while exponential functions increase or decrease by a constant percentage.

Front

What does a negative exponent indicate in an exponential function?

Back

A negative exponent indicates decay; for example, a function like f(x) = a(b^(-x)) shows that the quantity decreases as x increases.

Front

How can you identify an exponential function from its equation?

Back

An exponential function has the form f(x) = a(b^x), where b is a positive constant not equal to 1.