There are many real-life applications of composition of functions that occur. One such application is change in the area of a circular oil spill. Oil is spilling from a well at a rate of 2,500 gallons per day. At this rate the radius of the circular pool of oil will change at a constant rate of 4 miles per day. a. Write an expression that represents the radius of the oil slick at time t, r days after the leak has started.b. What are the domain and the range of the radius? Explain your reasoning.c. Write an expression to represent the area in terms of the radius and explain how the relationship between the radius and the area of the pool represent the composition of the two functions
There are many real-life applications of composition of functions that occur. One such
application is change in the area of a circular oil spill. Oil is spilling from a well at a rate
of 2,500 gallons per day. At this rate the radius of the circular pool of oil will change at a
constant rate of 4 miles per day.
a. Write an expression that represents the radius of the oil slick at time t, r days after
the leak has started.
b. What are the domain and the range of the radius? Explain your reasoning.
c. Write an expression to represent the area in terms of the radius and explain how
the relationship between the radius and the area of the pool represent the
composition of the two functions
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