A thermometer is taken from an ice bath at 0 degrees celsius and placed in boiling water at 100 degrees celsius.
After 80 seconds, the thermometer reads 98 degrees celsius. Assume the thermometer acts as a first-order system. An oceanographer measures the response of this thermometer to a ramp function [a ramp function is defined as f(t) = at, where a is some constant]. She wishes to evaluate its suitability for measuring ocean temperatures in a probe to be lowered at a constant velocity from a vessel. If she places the thermometer in a bath whose temperature decreases linearly at the rate of 8 degrees celsius per 5 minutes for at least 10 minutes, how much error will the thermometer indicate after 5 min? The error is defined as the difference in temperature between the actual temperature of the bath and the temperature reading of the thermometer.