The resistivity of a conducting wire is the reciprocal of the conductivity and i

Question

The resistivity of a conducting wire is the reciprocal of the conductivity and is measured in units of ohm-meters (m). The resistivity of a given metal depends on the temperature according to the equation below where t is the temperature in °C. (t) = 20^e^(t-20) There are tables that list the values of (called the temperature coefficient) and 20 (the resistivity at 20°C) for various metals. Except at very low temperatures, the resistivity varies almost linearly with temperature and so it is common to approximate the expression for (t) by its first or second degree Taylor polynomial at t = 20.

For what values of t does the linear approximation agree with the exponential expression to within one percent? °C <_ t <_°C

Explanation / Answer

Best Answer:  _exp(T) = 20*e^[(T-20)] // exponential equation representing "close" match to real resistivity
_lin(T) = 20[1+(T-20)] // linear approximation

you need to solve

| _exp(T) - _lin(T) | <=0.01
or
-0.01 <= _exp(T) - _lin(T) <=0.01
or
-0.01/20 <= e^[(T-20) - [1+(T-20)] <= 0.01/20

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