Exponential Equations / Graphs

Front

What is an exponential equation?

Back

An exponential equation is a mathematical expression in which a variable appears in the exponent. It can be written in the form y = a(b^x), where 'a' is a constant, 'b' is the base, and 'x' is the exponent.

Front

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

Back

The 'a' represents the initial value or y-intercept of the function.

Front

What is the general form of an exponential growth equation?

Back

The general form of an exponential growth equation is y = a(1 + r)^x, where 'r' is the growth rate.

Front

What is the difference between exponential growth and exponential decay?

Back

Exponential growth occurs when a quantity increases by a constant percentage over time, while exponential decay occurs when a quantity decreases by a constant percentage over time.

Front

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

Back

To find the y-intercept of an exponential function, substitute x = 0 into the equation and solve for y.

Front

What does the base 'b' in an exponential function y = a(b^x) indicate?

Back

The base 'b' indicates the growth or decay factor. If b > 1, the function represents growth; if 0 < b < 1, it represents decay.

Front

What is the equation for a population that starts with 10 and grows by 15% daily?

Back

Front

In the equation y = 15(1.2)^x, what does the '1.2' represent?

Back

The '1.2' represents a 20% growth rate, as it indicates that the population increases by 20% each hour.

Front

What is the y-intercept of the function y = 18(3)^x?

Back

The y-intercept is (0, 18).

Front

How can you identify an exponential growth factor from a set of equations?

Back

An exponential growth factor can be identified by looking for a base greater than 1 in the equation of the form y = a(b^x).