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. For example, if a population doubles every year, it is experiencing exponential growth.

Front

What is exponential decay?

Back

Exponential decay occurs when a quantity decreases by a consistent percentage over a period of time. For example, radioactive substances decay at a rate proportional to their current amount.

Front

Write the general formula for exponential growth.

Back

y = a(1 + r)^t, where 'a' is the initial amount, 'r' is the growth rate, and 't' is time.

Front

Write the general formula for exponential decay.

Back

y = a(1 - r)^t, where 'a' is the initial amount, 'r' is the decay rate, and 't' is time.

Front

What does the base of an exponential function represent?

Back

The base of an exponential function indicates the growth or decay factor. A base greater than 1 indicates growth, while a base between 0 and 1 indicates decay.

Front

How do you determine the y-intercept of an exponential function?

Back

The y-intercept of an exponential function can be found by evaluating the function at t=0. For example, in y = a(1 + r)^t, the y-intercept is 'a'.

Front

What is the y-intercept of the function y = 7(5/4)^x?

Back

The y-intercept is 7, as it is the value of the function when x = 0.

Front

If a quantity doubles every week, what expression represents its size after 'n' weeks?

Back

The expression is y = a(2)^n, where 'a' is the initial size.

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 is the growth rate in the equation y = 6(1.14)^x?

Back

The growth rate is 14%, as indicated by the factor (1 + 0.14) in the equation.