Exponential Growth

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 the general form of an exponential function?

Back

The general form is y = a(b^x), where 'a' is the initial value, 'b' is the growth factor, and 'x' is the exponent.

Front

What does the y-intercept represent in an exponential function?

Back

The y-intercept is the value of y when x = 0, representing the initial amount before any growth occurs.

Front

How do you find the y-intercept of the function y = 100(2^x)?

Back

Substitute x = 0 into the equation: y = 100(2^0) = 100.

Front

What is the growth factor in the function y = 100(2^x)?

Back

The growth factor is 2, indicating that the quantity doubles with each increase of 1 in x.

Front

What is the growth factor in the function y = 20(5^x)?

Back

The growth factor is 5, meaning the quantity increases by a factor of 5 for each unit increase in x.

Front

If y = 10(5^x), what is the y-intercept?

Back

The y-intercept is 10, found by substituting x = 0: y = 10(5^0) = 10.

Front

What is the difference between linear and exponential growth?

Back

Linear growth increases by a constant amount, while exponential growth increases by a percentage of the current value, leading to faster growth over time.

Front

What is an example of exponential growth in real life?

Back

An example is population growth, where the number of individuals increases at a rate proportional to the current population.

Front

How can you identify an exponential function from a table of values?

Back

If the ratio of consecutive y-values is constant, the function is likely exponential.