Exponential Growth & 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 is the formula for exponential growth?

Back

The formula is y = a(1 + r)^x, where 'a' is the initial amount, 'r' is the growth rate, and 'x' is the time.

Front

What is the formula for exponential decay?

Back

The formula is y = a(1 - r)^x, where 'a' is the initial amount, 'r' is the decay rate, and 'x' is the time.

Front

In the function f(x) = 800(0.85)^x, what does 800 represent?

Back

800 is the starting term or initial value of the function.

Front

In the function f(x) = 800(0.85)^x, what does 0.85 represent?

Back

0.85 represents the decay factor, indicating that the quantity decreases to 85% of its previous value.

Front

What is a y-intercept in a function?

Back

The y-intercept is the value of y when x = 0, representing the starting point of the function on a graph.

Front

How do you find the y-intercept of the function y = 720,500(1.022)^x?

Back

Substitute x = 0 into the function: y = 720,500(1.022)^0 = 720,500.

Front

Write an equation for a culture of bacteria that starts with 5000 cells and dies by 30% each year.

Back

y = 5000(0.7)^x.

Front

What does the term 'decay rate' mean?

Back

The decay rate is the percentage by which a quantity decreases over a specific period of time.