A case of vintage wine appreciates in value each year, but there is also an annual storage charge. The value of a typical case of investment-grade wine after t years is V(t) = 2000 + 40 t − 10t dollars (for 0 ≤ t ≤ 25). Find the storage time that will maximize the value of the wine.

You drop a rubber ball off the roof of a 50 meter high building onto a paved parking lot. it bounces back up with every bounce, but not quite all the way back up to you. after the first bounce it bounces back only 80 percent of the distance it was dropped from. the pattern continues, meaning after every bounce it comes up to just 80 percent of the previous maximum height. so if before the first bounce the height is 50 meters, what height does the ball reach after the fifth bounce? round your answer to one decimal place and chose the correct response from the choices below:

The tuition costs, c, for a local community college are modeled by c(h) = 250 + 200h, where h represents the number of credit hours taken. the local state university has tuition costs, s, modeled by the function s(h) = 300 + 180h. how many credit hours will a student have to take for the two tuition costs to be equal? round the answer to the nearest tenth of an hour.

Mr. thompson is on a diet. he currently weighs 260 pounds. he loses 4 pounds per month. what part of the story makes the relationship not proportional?