NBA Salary Growth: Solving for Average Salary and Future Projections

[courtrigrad]

If the average salary $$S$$ of an NBA player is increasing and can be modeled by: $$\frac{dS}{dt} = \frac{1137.7}{\sqrt{t}} + 521.3$$ and $$t = 5$$ is 1985.

a. Find the salary function in terms of the year if the average salary in 1985 was $325,000.
b. If the average salary continues to increase at this rate, in which year will the salary be $4,000,000?

Would I use the Mean Value Thoerem?

Any help is appreciated

Thanks

 

[scholzie]

Have you done any work on this problem yet? Do you know what the answer is supposed to be for part b?

 

[Justin Lazear]

Why would you use the Mean Value Theorem? You have an easily separable DEQ with the initial condition S(5) = 325000. Just solve it for S(t), and then find S^-1(4000000).

--J

 

[scholzie]

Why would you use the Mean Value Theorem? You have an easily separable DEQ with the initial condition S(5) = 325000. Just solve it for S(t), and then find S^-1(4000000).

--J

Correct me if I'm missing something here, but the equation has dS/dt and t in it, making it simply a first derivative. All that's needed is integrating the expression, and then setting the expression equal to S(5) and finding the constant of integration.

I'm not seeing where you're getting a Diff Eq from, when the equation doesn't contain a variable and it's derivative.

 

[Justin Lazear]

Correct me if I'm missing something here, but the equation has dS/dt and t in it, making it simply a first derivative. All that's needed is integrating the expression, and then setting the expression equal to S(5) and finding the constant of integration.

I'm not seeing where you're getting a Diff Eq from, when the equation doesn't contain a variable and it's derivative.

S'pose you're right. Either way, it doesn't really matter what you call it. The problem's trivial, whether or not you decide to bring the dt to the other side before you integrate.

--J

 

[scholzie]

S'pose you're right. Either way, it doesn't really matter what you call it. The problem's trivial, whether or not you decide to bring the dt to the other side before you integrate.

--J

It's no big deal... different strokes for different fo'ks. I was just scared I was missing something, but we're on the same page

 

[Justin Lazear]

I really don't understand why we wouldn't call it a differential equation! It's got the derivative, which is enough for me! But the definition is what the definition is, so. ;)

--J

 

[dextercioby]

He may very well integrate with corresponding limits.
$$\int_{325000}^{S}dS=\int_{5}^{t} dt \ f(t)$$

It's the most direct way.

Daniel.