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A wine dealer contemplates when to sell his bottle of wine for $30 today, or wait to sell it in the future. If he sells it in the future, then he can...

  1. A wine dealer contemplates when to sell his bottle of wine for $30 today, or wait to sell it in the future. If he sells it in the future, then he can sell it for a higher price. However, the sooner he sells the bottle, the more time he will have to invest the money (at 5% interest compounded continuously) and perhaps make a bigger profit that way. The amount of money a wine drinker will pay for the bottle t years from now is 30(1 + 20√t).When is the good time to sell the wine?

(In this problem, you may use a calculator to do the computations, but aside of that, you must show all work. For example, if solving for the critical numbers of a function, you must write the equation to set the derivative equal to 0. If there are endpoints necessary to test for the domain of your function, you must do so. The only thing you can use your calculator for is for carrying out computations or solving an equation which you have explicitly written!) 

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