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## Homework Statement

My question: Can I turn this difference equation for R below, into a continuous function R(t)? I have no idea if, or how, I can. And I'd like to.

Equation derived from the following manufacturer statement on the thermal response of a thermistor to a fixed temperature:

*The time constant is the time in seconds required for the thermistor to change through 63.2 % of the difference between its initial and final body temperatures, when subjected to a step change in temperature*

Using a small delta_t, relative to the time constant, the response of the thermistor to a constantly changing temperature T(t) was approximated to a continuous curve, via upper and lower step response boundaries, then graphed, which I have included with the rest of my work below.

## Homework Equations

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3. The Attempt at a Solution [/B]

I don't know how to attempt this. As I said, I'd like to be able to get the continuous function R(t) for a given T = f(t). Thanks.