	For the graph shown below, determine a possible rule in the form     y=k-2 ×3^(h-x)
y=6 given points (0,0)

To find a possible rule in the form \( y = k - 2 \times 3^{h - x} \) using the given point \( (0, 0) \) and the additional information \( y = 6 \), follow these steps:

### Step 1: Substitute the point \( (0, 0) \) into the equation
Substitute \( x = 0 \) and \( y = 0 \) into the equation \( y = k - 2 \times 3^{h - x} \):

\[
0 = k - 2 \times 3^{h - 0}
\]

Simplify:

\[
0 = k - 2 \times 3^h
\]

This can be rearranged to solve for \( k \):

\[
k = 2 \times 3^h
\]

### Step 2: Use the information \( y = 6 \) to find \( k \) or \( h \)
Assume that when \( y = 6 \), \( x = 0 \) (if it applies to this case), then substitute \( y = 6 \) into the equation:

\[
6 = k - 2 \times 3^{h - x}
\]

Substitute \( x = 0 \):

\[
6 = k - 2 \times 3^h
\]

Now, substitute the expression for \( k \) from Step 1:

\[
6 = (2 \times 3^h) - 2 \times 3^h
\]

This simplifies to:

\[
6 = 0
\]

This doesn't work, which suggests that more information might be needed, or there's a condition related to the point \( y = 6 \) being for another value of \( x \). Could you confirm or clarify any other points or conditions for \( y = 6 \)?

Would you like to explore this further or clarify additional points? 

---

Here are 5 relative questions:

1. Is there any other point given for when \( y = 6 \)?
2. Does \( y = 6 \) apply for a specific value of \( x \)?
3. Are there any transformations in the equation that should be considered?
4. Could you specify whether the \( y = 6 \) corresponds to a certain point?
5. Should we explore the nature of \( h \) more deeply?

**Tip**: When solving for constants, check if additional conditions or constraints are given to avoid contradictions.

For the graph shown below, determine a possible rule in the form y = k - 2 × 3^(h - x) with the given points (0,0) and y=6.

Explore how to determine a possible rule in the form y = k - 2 × 3^(h - x) given the points (0,0) and y=6. This problem covers key concepts of exponential functions and algebraic equations. Suitable for students in Grades 10-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation