Exponential Function Problem Solving

The video tutorial explains how to write the equation of an exponential function given two points. It starts by introducing the standard form of an exponential function and setting up a system of equations using the given points. The tutorial then demonstrates solving for variables, cross-multiplying, and simplifying the equations. It further explains how to find the base and coefficient of the function, leading to the final equation. The importance of following the order of operations is emphasized to avoid common mistakes.

What is the first step in writing the equation of an exponential function when given two points?

• Set up a system of equations.

• Calculate the midpoint of the points.

• Identify the y-intercept.

• Find the slope of the line.

What is the standard form of an exponential function?

• y = a/x

• y = ax^2 + bx + c

• y = a * B^x

• y = mx + b

When substituting the first point (1, 6) into the exponential equation, what equation do we get?

• 6 = a + B

• 6 = a/B

• 6 = a * B^2

• 6 = a * B^1

What is the equation obtained by substituting the second point (4, 48) into the exponential function?

• 48 = a * B^2

• 48 = a * B^4

• 48 = a/B^4

• 48 = a + B^4

What is the next step after substituting the points into the exponential equation?

• Add the equations together.

• Solve for one of the variables.

• Multiply the equations.

• Graph the equations.

What is the purpose of setting the two equations equal to each other?

• To determine the y-intercept.

• To eliminate one of the variables.

• To solve for the x-intercept.

• To find the slope.

What operation is performed to simplify the equation 6/B = 48/B^4?

• Subtraction

• Addition

• Cross-multiplication

• Division

What is the value of B after solving the equation 6B^4 = 48B?

• 4

• 2

• 1

• 3

What is the cube root of 8, which helps find the base B?

• 2

• 1

• 4

• 3

What is the result of dividing 48 by 6 in the process of solving for B?

• 16

• 12

• 8

• 6