Writing Exponential Equations from Two Points

Front

What is the general form of an exponential function?

Back

The general form of an exponential function is y = ab^x, where 'a' is the initial value, 'b' is the base, and 'x' is the exponent.

Front

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

Back

The value of 'a' can be determined by substituting the coordinates of the point (x, y) into the equation y = ab^x and solving for 'a'.

Front

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

Back

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

Front

How can you find the base 'b' of an exponential function using two points?

Back

To find the base 'b', you can use the formula b = (y2/y1)^(1/(x2-x1)), where (x1, y1) and (x2, y2) are the two points.

Front

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

Back

The point (0, a) indicates the initial value of the function, which is the value of 'y' when 'x' is 0.

Front

How do you write an exponential function given two points?

Back

1. Identify the initial value 'a' from one of the points. 2. Use the second point to find the base 'b' using the formula for b. 3. Write the function in the form y = ab^x.

Front

What is the process to estimate the value of an exponential function at a given x?

Back

To estimate the value of an exponential function at a given x, substitute the value of x into the function y = ab^x and calculate the result.

Front

What is the relationship between the coordinates of two points on an exponential function?

Back

The coordinates of two points (x1, y1) and (x2, y2) on an exponential function can be used to derive the function's parameters 'a' and 'b'.

Front

How do you verify if a given exponential function passes through a specific point?

Back

To verify, substitute the x-coordinate of the point into the function and check if the resulting y-value equals the y-coordinate of the point.

Front

What is the importance of estimating values in exponential functions?

Back

Estimating values helps in understanding the behavior of the function and making predictions based on the model.