Questions: Use the graph of y=Ca^x to determine the constants C and a. c= (Type an integer or a simplified fraction.)

Use the graph of y=Ca^x to determine the constants C and a. c= (Type an integer or a simplified fraction.)
Transcript text: Use the graph of $\mathrm{y}=\mathrm{Ca}^{\mathrm{x}}$ to determine the constants C and a. \[ c= \] (Type an integer or a simplified fraction.)
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Solution

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Solution Steps

Step 1: Identify the given points

The graph passes through the points (0,9) and (1,3).

Step 2: Set up the equation with the first point

Substitute the point (0, 9) into the equation y = Cax: 9 = Ca0

Step 3: Solve for C

Since any number raised to the power of 0 is 1, we have: 9 = C * 1 Therefore, C = 9.

Step 4: Set up the equation with the second point

Substitute the point (1, 3) and C = 9 into the equation y = Cax: 3 = 9a1

Step 5: Solve for a

Simplify the equation: 3 = 9a Divide both sides by 9: a = 3/9 a = 1/3

Final Answer:

C = 9, a = 1/3

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