Thread: Generate an equation based on another one?

Hi, I am not sure what category this belongs, I suppose it is here.

Net investment is given by the expression I(t) = 140t3/4. Note that net investment represents the change in the capital stock that occurs at time t. Can you use this information to generate an equation for the capital stock as a function of time t?
Use your equation to consider the following: If K today(t=0) = 150,000, what will K be equal to in 10 years (t=10)?


I have no idea. Help please?

Originally Posted by domain07

Hi, I am not sure what category this belongs, I suppose it is here.

Net investment is given by the expression I(t) = 140t3/4. Note that net investment represents the change in the capital stock that occurs at time t. Can you use this information to generate an equation for the capital stock as a function of time t?
Use your equation to consider the following: If K today(t=0) = 150,000, what will K be equal to in 10 years (t=10)?


I have no idea. Help please?

Do you mean I(t)= 140(t^3)/4 or I(t)= 140 t^(3/4)? I'm going to assume the latter since the former would be more simply written I(t)= 35t^3.

Also I will assume that "K" is "capital stock" although it would have been a good idea to say so!

If I(t) is the instantaneous rate of change of K(t), the derivative, then K(t) is the anti-derivative of I(t). Do you know the anti-derivative of t^n? If not, I may be completely misunderstanding your question.