the value V of a bottle of a certain rare wine is increasing at a rate of 3(sqrt(2t+1)) dollars per year when the wine is t years old. initially the wine was sold for $25 per bottle. How much will this wine be worth after 5 years?

Question

anonymous · Answer

56.84

anonymous · Answer

can you shoe me how to do it?

anonymous · Answer

Just substitute t=0, 1, 2, 3 and 4 into that equation, add them all up and add 25

anonymous · Answer

here's how to solve it on the web: http://www.wolframalpha.com/input/?i=Sum%5B3+*+Sqrt%5B2t+%2B+1%5D%2C+%7Bt%2C+0%2C+4%7D%5D+%2B+25

anonymous · Answer

what is this formula called? something sumation?

anonymous · Answer

just a summation

anonymous · Answer

does fundamental theorem works?

anonymous · Answer

what fundamental theorem?

anonymous · Answer

Oh wait are you in calculus?

anonymous · Answer

If so you should do a proper integral - I'll change it...

anonymous · Answer

of calculus

anonymous · Answer

yes

anonymous · Answer

That sum was for discrete values. an integral is a continuous sum

anonymous · Answer

just change the word 'sum' to 'integrate': http://www.wolframalpha.com/input/?i=Integrate%5B3+*+Sqrt%5B2t+%2B+1%5D%2C+%7Bt%2C+0%2C+4%7D%5D+%2B+25

anonymous · Answer

actually in that case the upper limit should probably be 5 instead of 0

anonymous · Answer

http://www.wolframalpha.com/input/?i=Integrate%5B3+*+Sqrt%5B2t+%2B+1%5D%2C+%7Bt%2C+0%2C+5%7D%5D+%2B+25

anonymous · Answer

so the answer is 24 + 11Sqrt[11], or 60.48

anonymous · Answer

ok thanks

anonymous · Answer

how do i take the integral of 3[\sqrt{2t+1
}\]

anonymous · Answer

http://i.imgur.com/unI7k.gif

anonymous · Answer

thanks for helping

anonymous · Answer

i hope this was helpful