Exponential Growth & 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 describes a decrease in quantity where the rate of decrease is proportional to the current amount, resulting in a rapid decline that slows over time.

Front

What does the variable 'a' represent in the function f(x) = a(b)^x?

Back

The variable 'a' represents the initial amount or starting value in the exponential function.

Front

What does the variable 'b' represent in the function f(x) = a(b)^x?

Back

The variable 'b' is the base of the exponential function, representing the growth (b > 1) or decay (0 < b < 1) factor.

Front

How do you identify exponential growth from a function?

Back

Exponential growth can be identified if the base 'b' in the function f(x) = a(b)^x is greater than 1.

Front

How do you identify exponential decay from a function?

Back

Exponential decay can be identified if the base 'b' in the function f(x) = a(b)^x is between 0 and 1.

Front

What is the common ratio in the function f(x) = 300(1.16)^x?

Back

The common ratio is 1.16, indicating a 16% increase for each unit increase in x.

Front

If a function is modeled as A = 1200(0.85)^6, what type of model is it?

Back

This model represents exponential decay because the base 0.85 is less than 1.

Front

What is the formula for calculating the future value in exponential growth?

Back

The formula is A = P(1 + r)^t, where A is the future value, P is the principal amount, r is the rate of growth, and t is the time.

Front

What is the formula for calculating the future value in exponential decay?

Back

The formula is A = P(1 - r)^t, where A is the future value, P is the principal amount, r is the rate of decay, and t is the time.