Question

An oil tanker has hit a sand bar and ripped a hole in the hull of the ship. Oil has begun leaking from the tanker. The oil is leaking from the ship forming a circle around it. The radius of the circle is increasing at a rate of 2.3 feet per hour. Please assist the Wild Life Federation with the following calculations. Thank you in advance for your assistance. (Round all answers to the nearest tenths place unless otherwise specified, use the π button on your calculator for calculations.) 1) A) Write the radius of the circle as a function of time. Use t as the symbol to represent time (you will need to use the information found in the news clip above.) B) What is the radius of the circle after 2 hours? C) What is the radius of the circle after 2.5 hours? D) If the oil tanker is 250 yards from shore, when will the oil first reach the shoreline? (Remember to convert to feet) 2) Write the area of the circle as a function of the radius. Use the symbol r to represent the radius. 3) A) Using the functions found in questions 1 and 2, write a function that represents area as a function of time. B) What is the area of the circle after 2 hours? C) What is the area of the circle after 2.5 hours? D) What is the area of the circle after 3 hours? E) What is the area of the circle after 3.5 hours? Math 171 Unit 1 Lab 4) Compute the average rate of change per hour for the area from 2 to 2.5 hours. 5) Compute the average rate of change per hour for the area from 3 to 3.5 hours. 6) Based upon the results found in questions 4 and 5 what is happening to the average rate of change of the area of the circle as time passes? (Increasing, Decreasing, Constant?) 7) If the tanker is 250 yards from the shore, how long will it be until 8 miles of shoreline is contaminated with oil? Round to the nearest number of days. (For the benefit of this problem, the shore is straight and if you were to draw a line perpendicular to the shore 250 yards you would find the boat, the spread will be 4 miles to either side of the ship, refer to the diagram below. Hint 1mi=5280 ft.) A) Use the figure below and find the length of the radius in feet. B) Using your formula from problem 1A, find the time in hours. C) The original question asks for the time measured in days. Convert your answer from 7B to days, rounding to the nearest number of days. Radius Radius 250 yds 4 miles 4 miles

Answer 1