Exponential Growth or 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. The general formula is f(x) = a(b)^x, where b > 1.

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. The general formula is f(x) = a(b)^x, where 0 < b < 1.

Front

Identify the common ratio in the function: f(x) = 200(0.5)^x.

Back

The common ratio (b) is 0.5.

Front

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

Back

The 'a' represents the initial value or starting amount when x = 0.

Front

What is the y-intercept of the function f(x) = 5(3)^x?

Back

The y-intercept is 5, which is the value of f(0).

Front

Classify the model A = 1500(0.9)^t as growth or decay.

Back

This model represents exponential decay.

Front

What is the formula for calculating exponential growth?

Back

The formula is f(t) = 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 calculating exponential decay?

Back

The formula is f(t) = 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 growth is this?

Back

This is an example of exponential growth.

Front

What is the half-life in the context of exponential decay?

Back

Half-life is the time required for a quantity to reduce to half its initial value.