# Composite function help: the speed of the boat is represented by s(t)=8 + t + 0.2t^2

#### helpmepls12

##### New member
A prospective boat owner wants to determine the approximate dollar cost per hour of operating a particular boat. The manufacturer states the speed of a boat, s in kilometers per hour, at time t in hours after the boat is under way, is represented by s(t)=8 + t + 0.2t2. At the current cost of diesel fuel, the dollar cost per kilometre of traveling at speed s kilometres per hour is represented by c(s)=(0.01s-0.7)2+0.5 .
a) Form an algebraic expression for c(s(t)), the cost of operating the boat as a function of time. (expansion is not needed) (2A)
b) What does c(s(t)) mean in context of this problem? (2C)
c) Determine the cost per km, 5 hours into a trip under the above conditions.

for a), I got c(s(t))= (((0.01)(8+t+0.2t^2))-0.7)^2 +0.5
b) I'm guessing that it means that its the cost of operating the boat per hour?
c) Fo i just plug in 5 for the composite function i created?

pls help

#### stapel

##### Super Moderator
Staff member
A prospective boat owner wants to determine the approximate dollar cost per hour of operating a particular boat. The manufacturer states the speed of a boat, s, in kilometers per hour, at time t in hours after the boat is under way, is represented by s(t) = 8 + t + 0.2t2. At the current cost of diesel fuel, the dollar cost per kilometre of traveling at speed s kilometres per hour is represented by c(s) = (0.01s - 0.7)2 + 0.5.

a) Form an algebraic expression for c(s(t)), the cost of operating the boat as a function of time.

for a), I got c(s(t))= [{(0.01)(8+t+0.2t2)} - 0.7]2 + 0.5
Yes.

b) What does c(s(t)) mean in context of this problem?

b) I'm guessing that it means that its the cost of operating the boat per hour?
Since "c" stands for "cost in terms of" and since the input variable "t" stands for "time", then, yes, this is "cost in terms of time".

c) Determine the cost per km, 5 hours into a trip under the above conditions.

c) For i just plug in 5 for the composite function i created?
Since "t" stands for "time" and since they've asked you to evaluate at a given time, yes, you would plug the time value in for the variable for time. Since "c" stands for "cost in terms of" and since they've asked you for the corresponding cost, yes, you would plug the time value into the cost equation.