Suppose a body has temperature B and is cooling toward room temperature of 20°C according to the function B(t) = 20 + 17e-t where t is measured in hours. A $ 10 thermocouple can detect a difference of 0.1°C, a $100 thermocouple can detect a difference of 0.01°C, and so forth.
a. How much would it cost to detect the difference after 1 h?
b. How much would it cost to detect the difference after 5 h?
c. How much would it cost to detect the difference after 10 h?
Scientifically, two quantities are close if it requires an accurate measuring device to detect the difference. In real life, accuracy costs money. How much would it cost to measure the differences in the above circumstances?