Question

The function f(x) = 2x2 3 represents the rate of a boat traveling with the current in miles per hour. The function g(x) = x 2 represents the time the boat traveled in hours. Solve (f • g)(2), and interpret the answer. (f • g)(2) = 15, the distance in miles the boat traveled (f • g)(2) = 15, the number of boats (f • g)(2) = 44, the distance in miles the boat traveled (f • g)(2) = 44, the number of boats.

Answer 1

The distance in miles the boat traveled for the modeled function of speed and time is,

$(f .g)(2) = 44$

What is the rate of speed?

The rate of speed is the rate at which the total distance is travelled in the time taken.

The function which represents the rate of a boat traveling with the current in miles per hour is,

$f(x) = 2x^2+ 3$

The function which represents the time the boat traveled in hours is,

$g(x) = x+ 2$

The distance traveled by boat is the product of rate of speed of the boat and time taken by the boat. Thus, the multiplication function for the above two function can be given as,

$(f.g)(x)=(2x^2+3)(x+2)$

Solve the above function for (f • g)(2) as,

$(f.g)(2)=(2(2)^2+3)(2+2)\\(f.g)(2)=(8+3)(4)\\(f.g)(2)=44$

Interpret the above answer with the given option we get,  (f • g)(2) = 44, the distance in miles the boat traveled

Hence, the distance in miles the boat traveled for the modeled function of speed and time is,

$(f .g)(2) = 44$

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