How can I correctly find my t when working with DeltaTimes?

I am currently storing an ever growing series of positions in a table, From the Most recent [1] to the earliest entry [n] I know that the time between registering each of these positons will always be X

To smoothly lerp between them, I am using the Heartbeat element of RenderStepped which gives us a delta time. Using the delta time, knowing that time between positions will always be X, what should I be doing?

Code looks like this;

    totaldt = totaldt+dt--/X
    if totaldt > X then--if its over the deisred amount, we don't need
        totaldt = X-totaldt -- gives us a number thats <0>
    end
    if pos~=positions[1] then --If we changed our first entry (shifted all by one)
        pos=positions[1]
        total = X-totaldt
    end
    local t = totaldt/X -- exists between 0-1 (or slightly outside, but never massively.)