Writing Exponential Equations from Two Points

Front

What is the general form of an exponential function?

Back

y = ab^x, where a is the initial value and b is the base.

Front

How do you determine the value of 'a' in an exponential function from a point (x,y)?

Back

The value of 'a' is the y-coordinate when x = 0.

Front

What does the base 'b' represent in an exponential function?

Back

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

Front

Given points (0, a) and (x, y), how can you find 'b'?

Back

Use the formula b = (y/a)^(1/x).

Front

What is the significance of the point (0, a) in an exponential function?

Back

It indicates the initial value of the function when x = 0.

Front

How can you write an exponential function from two points?

Back

1. Identify 'a' from the first point (0, a). 2. Use the second point to find 'b' using the formula.

Front

If a function passes through (0, 10) and (2, 160), what is 'a'?

Back

a = 10.

Front

If a function passes through (0, 13) and (2, 325), what is 'b'?

Back

b = 5.

Front

What is the first step in writing an exponential function from two points?

Back

Identify the initial value 'a' from the point where x = 0.

Front

How do you verify if a function is exponential?

Back

Check if the ratio of the outputs (y-values) is constant for equal intervals of the inputs (x-values).