Which equation represents an exponential function with an initial value of500500500?

Step 1: Define the Problem

Identify the key components of the question:

• We need to find an equation that represents an exponential function.
• The function must have an initial value of 500.

Step 2: Break Down the Problem

Divide the problem into smaller parts:

• Understand the general form of an exponential function.
• Determine how the initial value is represented in this form.

Step 3: Apply Relevant Concepts

Use appropriate academic theories or formulas:

• The general form of an exponential function is $f(x) = a \cdot b^x$, where:
  • $a$ is the initial value.
  • $b$ is the base of the exponential function.
• Given that the initial value is 500, we have $a = 500$.

Step 4: Analysis, Verify and Summarize

• The equation representing the exponential function with an initial value of 500 is $f(x) = 500 \cdot b^x$.
• The base $b$ can be any positive real number other than 1, depending on the specific growth or decay rate desired.

Final Answer

The equation representing an exponential function with an initial value of 500 is:

$f(x) = 500 \cdot b^x$

where $b$ is a positive real number.