Resistance in copper wire: Electric resistance in copper wire changes with the temperature of the wire. If C(t) is the electric resistance at temperature t, in degrees Fahrenheit, then the resistance ratio C(t)/C(0) can be measured.
a. On the basis of the data in the table, explain why the ratio C(t)/C(0) can be reasonably modeled by a quadratic function.
b. Find a quadratic formula for the ratioC(t)/C(0) as a function of temperature t.
c. At what temperature is the electric resistance double that at 0 degrees?
d. Suppose that you have designed a household appliance to be used at room temperature (72 degrees) and you need to have the wire resistance inside the appliance accurate to plus or minus 10% of the predicted resistance at 72 degrees.
i. What resistance ratio do you predict at 72 degrees? (Use four decimal places.)
ii. What range of resistance ratios represents plus or minus 10% of the resistance ratio for 72 degrees?
iii. What temperature range for the appliance will ensure that your appliance operates within the 10% tolerance? Is this range reasonable for use inside a home?
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