Algebra-equation to model balloon's elevation as function of time (t)

In summary, to set up an equation to model a balloon's elevation as a function of time, you need to identify the variables involved (elevation and time), determine the relationship between them (direct), and use the equation y = mx + b, where y represents elevation, m represents rate of change, x represents time, and b represents initial elevation. The rate of change can be determined by dividing the change in elevation by the change in time. A quadratic equation can also be used to model a balloon's elevation if it follows a curved path. To predict the balloon's elevation at a certain time, plug in the value of time into the equation. The equation can also be used to model a balloon's descent by changing the relationship between
  • #1
yamuna
4
0
Algebra--equation to model balloon's elevation as function of time (t)

Homework Statement



Balloon takes off from a location 158ft. above sea level. it rises 56 ft/min.

Please help me write an equation to model balloon's elevation h as function of time t

Homework Equations





The Attempt at a Solution



t=158h + 56
 
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  • #2


Let's take this one step at a time. You know the formula for modeling something that changes with time is F(t) = Changing Variable times t + Initial State, right?

If you know the Initial State (Height) of the Balloon, then what else needs to be placed in the function?

Set F(t) to the height.
Set time to t.
Set Initial State to 158.

So far we got h = ? + 158

What are we missing?
 
  • #3


Thanks for your reply.

What is missing in the equation is 56 ft./min.
Then, the ans could be
h= 56t + 158

Right?

Y
 
  • #4


That is correct.
 
  • #5
Welcome to PF!

Hi TheShehanigan! :smile:

Nice one! :wink:

Welcome to PF! :biggrin:
 

FAQ: Algebra-equation to model balloon's elevation as function of time (t)

How do you set up an equation to model a balloon's elevation as a function of time?

To set up an equation, you first need to identify the variables involved. In this case, the variables are the balloon's elevation and time. Then, you need to determine the relationship between the two variables. In this situation, the balloon's elevation increases as time passes, so it is a direct relationship. Finally, you can use the equation y = mx + b to model the balloon's elevation, where y represents the elevation, m represents the rate of change, x represents time, and b represents the initial elevation.

How do you determine the rate of change in the equation for a balloon's elevation?

The rate of change, represented by the variable m, can be determined by dividing the change in elevation by the change in time. This can be calculated by taking the difference between two points on the graph and dividing it by the difference in time between those points.

Can you model a balloon's elevation with a quadratic equation?

Yes, it is possible to model a balloon's elevation with a quadratic equation. A quadratic equation takes the form of y = ax^2 + bx + c, where a, b, and c are constants. This type of equation can be used if the elevation of the balloon follows a curved path instead of a straight line.

How can you use the equation to predict the balloon's elevation at a certain time?

To predict the balloon's elevation at a certain time, you can plug in the value of time into the equation and solve for the elevation. This will give you the estimated elevation at that specific time.

Can the equation be used to model a balloon's descent?

Yes, the equation can be used to model a balloon's descent by changing the relationship between the variables. In this case, the elevation of the balloon would decrease as time passes, so it would be an inverse relationship. The equation would then be y = -mx + b, where m represents the rate of descent and b represents the initial elevation.

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