Writing Exponential Equations from Two Points

Front

What is an exponential function?

Back

An exponential function is a mathematical function of the form y = ab^x, where a is a constant, b is the base (a positive real number), and x is the exponent.

Front

What does the 'a' represent in the exponential function y = ab^x?

Back

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

Front

What does the 'b' represent in the exponential function y = ab^x?

Back

The 'b' represents the growth (if b > 1) or decay (if 0 < b < 1) factor of the exponential function.

Front

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

Back

The y-intercept can be found by evaluating the function at x = 0, which gives y = a.

Front

Given points (0, 13) and (5, 416), how do you determine the exponential function?

Back

Use the point (0, 13) to find 'a' (y-intercept), then use the second point to solve for 'b'.

Front

What is the general form of an exponential equation?

Back

The general form of an exponential equation is y = ab^x.

Front

How do you determine if a function is exponential?

Back

A function is exponential if it can be expressed in the form y = ab^x, where b is a positive constant.

Front

What is the significance of the base 'b' in an exponential function?

Back

The base 'b' determines the rate of growth or decay of the function.

Front

If a function passes through (0, 2), what is the y-intercept?

Back

The y-intercept is 2.

Front

How do you write an exponential function from two points?

Back

Identify the y-intercept from one point, then use the second point to solve for the base 'b'.