Final answer:
The rate of oil leakage from a ruptured tanker is 65 thousand liters per minute at t=0. It decreases to about 0.2936 thousand liters per minute at t=60 as per the given exponential decay function. To find the total oil leaked in the first hour, one would integrate this rate function from t=0 to t=60.
Step-by-step explanation:
A student has asked about the rate at which oil is leaking from a ruptured tanker and the total amount of oil leaked during the first hour. The leak rate is given by the function r(t)=65e⁻⁰ˠ⁰⁹ᵗ in thousands of liters per minute.
Calculating the Leak Rates
At t=0, the rate is simply r(0) which gives us 65 thousand liters per minute, as there is no decay factor at the start (e to the power of 0 is 1).
At t=60, the rate is calculated as r(60) = 65e⁻⁰ˠ⁰⁹×60 which results in approximately 0.2936 thousand liters per minute.
Finding Total Oil Leaked in the First Hour
To determine the total amount of oil leaked during the first hour, we need to integrate the leak rate function r(t) with respect to time from t=0 to t=60 minutes. This calculation yields the total volume of oil lost in thousands of liters.
Note: As this is a hypothetical example, the actual integral calculation to find the total volume of oil leaked over the hour is not included, since it wasn't originally provided in the question and requires integration techniques.