Advanced Functions: Construct Table & Limitations

[ohhnana]

Homework Statement

A particular power boat traveling at V0 km/h when its power is turned off will have its speed V given by V(t) = V0 × 10-0.18t where t is the time in seconds since the engine was turned off. If this boat was traveling at 50km/h before powering down, construct a table showing its speed at t = 0, 1, 2, ..., 5. What are the limitations in using this exponential function to describe the speed of the boat?

Homework Equations

A=A0(1+i)^n

The Attempt at a Solution

V(t)=V0*10^-.18t
=50*10^-.18t

 

[Mentallic]

Ok so you have the equation of the speed of the boat, given $$v(t)=50\cdot 10^{-0.18t}$$ so now for your attempt at the solution, what is the speed of the boat at those given time intervals?

 

[ohhnana]

what do u mean what is the speed of the boat at those given time intervals? like the time?

 

[Mentallic]

No, not like the time, like the speed. Notice this part in your question:

construct a table showing its speed at t = 0, 1, 2, ..., 5.

What is the speed at t=0? Now, what is the speed at t=1. etc.

 

[HallsofIvy]

In other words, replace t in the formula by 0 and do the arithmetic. Then replace t in the formual by 1 and do the arithemetic. Then do t= 2, 3, 4, and 5.

 

[Mentallic]

In other words, replace t in the formula by 0 and do the arithmetic. Then replace t in the formual by 1 and do the arithemetic. Then do t= 2, 3, 4, and 5.

I find it quite perplexing that this needs to be explained while the OP is studying exponentials.

 

[ohhnana]

oh ok i get that part but how will find the limitations

 

[Mentallic]

I'm unsure. What has your class talked about in regards to this? Because it could be anything ranging from it only works for t>0, to the waves and other forces affect the boat and thus the equation isn't exactly perfect.

 

[eumyang]

I have an idea regarding the limitations of using the exponential function: this power boat, with the engine turned off, will eventually stop. Can this function properly model the stop, technically?

 

[HallsofIvy]

If you define "stopping" to mean that the speed is less than some specific error in measuring speed, then the exponential will give a very accurate model.