Prompt No calculator is allowed on this question. An oil spill has occurred in the Gulf...

Transcribed Image Text:

Prompt No calculator is allowed on this question. An oil spill has occurred in the Gulf of Mexico. As the oil pours into the gulf, it rises up to float on top of the water, forming an oil slick. The shape of the resulting oil slick can be approximated with a circle a. What is the rate of change of the area of the oil slick when the radius is 1000 ft and dr 25 ft/hr? Indicate units of measure. dt b. If the radius R(t) of the oil spill is growing at a rate of dR dt 250t ft/hr, write an integral expression for the radius R(t) of the spill at t = 5 hours. Use this expression to calculate the radius of the spill at t = 5 hours. c. Given the function for R(t) from part (b), evaluate: 5 L A'(t) at 0 Using appropriate units, interpret the meaning of the integral in terms of the area of the oil spill. Prompt No calculator is allowed on this question. An oil spill has occurred in the Gulf of Mexico. As the oil pours into the gulf, it rises up to float on top of the water, forming an oil slick. The shape of the resulting oil slick can be approximated with a circle a. What is the rate of change of the area of the oil slick when the radius is 1000 ft and dr 25 ft/hr? Indicate units of measure. dt b. If the radius R(t) of the oil spill is growing at a rate of dR dt 250t ft/hr, write an integral expression for the radius R(t) of the spill at t = 5 hours. Use this expression to calculate the radius of the spill at t = 5 hours. c. Given the function for R(t) from part (b), evaluate: 5 L A'(t) at 0 Using appropriate units, interpret the meaning of the integral in terms of the area of the oil spill.