Understanding the Meaning of 'a' in Exponential Decay Model

[shad0w0f3vil]

Homework Statement

In the standard model for exponential decay, y=ab^x , what does a represent and why?

The Attempt at a Solution

I know that a is the value of y when x=0, but I don't understand why this is the case. Any help would be appreciated, thanks.

 

[Defennder]

You mean b^(-x). And you've already answered the question yourself.

 

[shad0w0f3vil]

but i don't understand why though.

 

[futurebird]

What is $$ab^{0}$$ equal to? (As long as $$b \neq 0$$)

 

[shad0w0f3vil]

is it just a?

 

[futurebird]

is it just a?

Yup. You get that part right?

In this kind of question you want to say what each variable or constant stands for. And then describe how the value of the function changes as x changes.

 

[shad0w0f3vil]

yeh, what else am I missing?

 

[futurebird]

x stands for time, so when x=0 we know that $$y=a$$ so that's why a is the initial value. As x increases what will happen to $$y=ab^{-x}$$? will it get smaller or larger? why?

 

[shad0w0f3vil]

actually in our case b represents the decay factor, as a result the x is positive. However, as x increases b would get smaller (for the model i just said), meaning that when it is multiplied to a, the value of y would decrease as x increases.