Can someone explain what f(x)=ab^x+c means variably and how to use?

Question

anonymous · Answer

The question doesn't make sense.

What is means "variably"?  I don't know what you're asking here.

anonymous · Answer

I mean what does each variable mean?

anonymous · Answer

I'm trying to figure out a body temperature decay graph from some info our teacher gave us, but I can't because I don't understand the equation.

anonymous · Answer

Okay so... $$ \Large
f(x) = ab^x+c
$$Since the input variable $x$ is used as an exponent, we call this an exponential function.

When $x=0$, $b^x = 1$, so the initial value is going to be $a+c$.

anonymous · Answer

The function is growing by a factor of $b$.

anonymous · Answer

It's kinda hard to explain stuff when I don't know what you want to be explained.

anonymous · Answer

What do a and c represent? Like is a the initial temperature of the room or the body? (there's a dead body and we're trying to figure out how long it has been dead, or cooling)

anonymous · Answer

Okay, so since it's body temperature, it's going to be cooling.

This means that $b<1$ because otherwise body temp would be rising.

When an exponential function is decreasing, it normally (when it doesn't have an offset like $+c$) converges at $0$.
So this function must be converging at $c$.  Thus $c$ is the room temperature.

Since the initial value is $a+c$, that means the body temperature is $a+c$.
This would mean that $a$ is going to be the difference in temperature between the room and the body.

We know $b<1$.  Suppose $x$ is in hours and $b=1/2$.  That would mean for every hour, the difference in temperature is half what it used to be.

anonymous · Answer

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