Chapter 5.5, Problem 10E

Reminder Round all the answers to two decimal places unless otherwise indicated.

Resistance in Copper Wire Electric resistance in copper wire changes with the temperature of the wire. If $C\left(t\right)$ is the electric resistance at temperature $t$, in degrees Fahrenheit, then the resistance ratio $C\left(t\right)/C\left(0\right)$ can be measured.

Temperature $t$, in degrees	$\frac{C\left(t\right)}{C\left(0\right)}$ ratio
$0$	$1$
$10$	$1.0393$
$20$	$1.0798$
$30$	$1.1215$
$40$	$1.1644$

a. Use regression to find a quadratic formula for the ratio $C\left(t\right)/C\left(0\right)$ as a function of temperature $t$. Do not round the regression parameters.

b. At what temperature is the electric resistance double that at $0$ degrees?

c. 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 that $10\%$ tolerance? Is this range reasonable for use inside a home?