Writing Exponential Functions

The video tutorial explains how to write an exponential function that passes through two given points on the XY coordinate plane. It involves multiple steps, starting with solving for 'a' and 'b' in the equation y = a * b^x. The process includes substituting the given points into the equation, solving for 'a' by isolating it, and then using the second point to solve for 'b'. The tutorial emphasizes understanding fractions and the importance of each step in reaching the final solution, which is the exponential function y = 1/2 * 2^x.

What is the main goal of the problem discussed in the video?

• To calculate the area under a curve

• To determine the intersection of two lines

• To find the slope of a line

• To write an exponential function passing through two points

What is the form of the exponential function we are trying to find?

• y = mx + c

• y = ax^2 + bx + c

• y = a * b^x

• y = a / b^x

When substituting the first point (2, 2) into the equation, what expression do we get for 'a'?

• a = 2 * b^2

• a = 2 / b^2

• a = 2 + b^2

• a = b^2 / 2

What is the next step after finding 'a' in terms of 'b' using the first point?

• Substitute the second point into the equation

• Check the solution with a calculator

• Solve for 'b' directly

• Graph the function

What is the value of 'x' when substituting the second point (3, 4) into the equation?

• 4

• 2

• 3

• 5

What mathematical operation is primarily used to simplify the equation with the second point?

• Multiplication

• Addition

• Division

• Subtraction

What is the simplified form of b^3 / b^2?

• b^3

• b^2

• b

• b^5

After solving for 'b', what is its value?

• 4

• 2

• 1

• 3

How do you calculate 'a' once 'b' is known?

• a = b^2 / 2

• a = b / 2

• a = 2 / b^2

• a = 2 * b^2

What is the final value of 'a' in the exponential function?

• 1

• 1/4

• 2

• 1/2