Question

The function C(g) = 2.75g represents the cost (in dollars) of g gallons of gasoline at a gas

station. The function g(m) 0.04m approximates the number of gallons of gasoline a vehicle uses to travel m

miles.

find C(g(m))

interpret the coefficient
HELP PLEASE

Answer 1

a. The value of C(g(m)) = 0.11m

b. The coeffient of C(g(m)) is the cost per mile of travel of the vehicle.

a. The function C(g(m))

The value of C(g(m)) = 0.11m

Since the function C(g) = 2.75g represents the cost (in dollars) of g gallons of gasoline at a gas station and the function g(m) = 0.04m approximates the number of gallons of gasoline a vehicle uses to travel m miles.

We need to find the function C(g(m))

So, substituting g(m) = 0.04m into C(g), we have

C(g) = 2.75g

C(g(m)) = 2.75(0.04m)

C(g(m)) = 0.11m

The value of C(g(m)) = 0.11m

b. The coeffient of C(g(m))

The coeffient of C(g(m)) is the cost per mile of travel of the vehicle.

The coeffient of C(g) is cost per gallon, since C(g)/g = 2.75 cost/gallon and the coefficient of g(m) is gallon per miles since g(m)/m = 0.04 gallon per mile.

Since the coeffient of C(g(m)) = coefficient of C(g) × coefficient of g(m), then

coeffient of C(g(m)) = 2.75 dollars/gallon × 0.04 gallon/mile = 0.11 dollars/mile

So, the coeffient of C(g(m)) is the cost per mile of travel of the vehicle.

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