What does the $A$ in $Y=A+Be^{CX}$ represent?

I'm a novice trying to learn about statistics in the infrastructure asset management industry.

I have an existing exponential regression equation that is used to find the condition of a given asset:

$${Y} = A + Be^{CX}$$

I'm trying to determine what each of the variables in that equation represent. Here is what I think I know:

• ${Y}$ is the asset condition.
• ${B}$ is $-1$, so it can be ignored.
  • I believe we use $-1$ so that the line will point downwards. Otherwise, exponential regression lines normally point upwards.
• $e$ is the inverse of the natural logarithm of a number.
• ${C}$ is an exponential regression coefficient.
• ${X}$ is the age of the asset in years.

Question:

I'm not sure about $A$. For my purposes, I believe the value would always be $21$, which is the maximum condition an asset can ever be ($20$), plus $1$.

But what does $A$ represent? Is it the $y$-intercept?

• If so, I find that confusing, because the asset condition can't ever be $21$. The maximum condition is $20$. So, I don't understand how the y-intercept could be $21$.

Solution 1:

My best guess:

$Be^{CX}$ is always going to be at least $1$ or greater. Even when the age is $0$, $Be^{CX}$ will still be $1$. The reason being, $e^0$ is equal to $1$, because any number to the power of zero equals $1$.

So, in order for the asset condition to be $20$ when the age is $0$ (when the asset is new/in perfect condition), we need to set $A$ to $21$ so that when we subtract $1$, $A$ will be $20$ (as expected).

Therefore, $A$ is the y-intercept, which is effectively $21 - 1$ (aka $Y(0) - B$).