solve(2*x + 5 = 0, x);Suppose that now we'd like to answer a question like: ``How long does it take a $1000 investment drawing 6% interest, compounded daily, to double in value?'' Answering this question involves setting up and solving equations, and solving equations is something at which Maple excels.
For example, let's solve a simple equation in one unknown:
| solve(2*x + 5 = 0, x); |
Notice that solve takes two parameters: the equation to be solved and the unknown to be solved for. If one side of the equation is 0 and if the equation only contains one unknown, there is a simpler form that saves typing:
| solve(2*x + 5); |
There is a related function called fsolve, that on the surface works much like solve:
| fsolve(2*x + 5); |
Whereas solve tries to solve equations symbolically to obtain an exact answer (much as you do), fsolve tries to solve them numerically, obtaining an approximate floating-point answer. The difference is probably a bit vague to you right now, but the important thing to know is that fsolve will solve more equations more efficiently, but not as accurately, than solve will.
It is worth illustrating this difference a bit. Below we use solve and fsolve to attempt to solve the same simple equation. Can you explain what happens?
| solve(cos(x) = x); |
| fsolve(cos(x) = x); |
Now back to the question we posed at the beginning of this section. We can answer it quite easily by using solve:
| solve(intervals(1000, .06, years, 365) = 2000); |
It turns out that the amount of time that it takes an investment to double is independent of the original investment. Below, we use the symbol balance in place of the number 1000:
| solve(intervals(balance, .06, years, 365) = 2*balance, years); |
Let's compare that to the amount of time required for the investment to double with only annual compounding:
| solve(compound(balance, .06, years) = 2*balance, years); |
Notice here that solve can deal with the functions compound and intervals--which you defined--just as easily as it can deal with the functions that it defines. And so can you. Perhaps you've even forgotten at this point how the functions were derived. It doesn't really matter. All that is important is that you remember how to use them.