A red wine’s value depends on the length of time it is aged in oak casks before it is bottled. If the relationship between the value of the wine and its length of time in oak casks is given by
Value in terms of today’s dollars = $(10 + 5 ln( t + 1)), where t is measured in years.
To the nearest tenth of a year, how long will the wine be aged if the interest rate is 4%?
To the nearest tenth of a year, how long will the wine be aged if the interest rate is 2.52%?
Is the interest rate in this problem a “real” or “nominal” interest rate? Explain.
Though you can do this problem with pencil and paper and a calculator, it may be easiest to do it in a spreadsheet. Though not necessary, the first derivative of the value with respect to t (i.e., the slope of the value line at any single point) is = 5/(t+1).
How critical was the Black Death for painting in Siena, Florence and Padua in the second 50% of the fourteenth century? From 1280 until the appearance of the Black Death, Florence, Siena and Padua had been developing in riches and size, however the flare-up of sickness in 1348 and the years following prompted the passings of between a half and 66% of their populaces (Norman, 1995, II, 8). This 'cataclysmic fall' prompted the climax of many building ventures, strikingly the development of the Duomo Nuovo in Siena (Norman, 1995, II, 135), however the centrality of the Black Death as for painting is questioned. Since the distribution of Meiss' work, Painting in Florence and Siena After the Black Death (1951), the association between the Black Death and an adjustment in craftsmanship amid the second 50% of the fourteenth century has been the subject of exchange among workmanship students of history. Henk Van Os, for instance, contends that Meiss was not the first to distinguish this pattern, but rather that he was the first to ascribe it to the social and religious change which went with the Black Death (Van Os, 1981, 238). There has been much exchange concerning whether the Black Death could be viewed as an incredible definitive occasion that Meiss affirmed. The discussion centers around three critical territories of thought: right off the bat, regardless of whether the works that Meiss refers to are effectively dated (i.e. regardless of whether they can with sureness be set previously or after 1348); besides, whether the Black Death was really a causative factor in the apparent change in style; and, thirdly, whether there was one move or a few in the aesthetic course of the fourteenth century. In perspective of these debate, we should be careful with adopting excessively shortsighted a strategy. For a case of the main component of this discussion, we can look to the Triumph of Death in the Camposanto at Pisa and Barna da Sierra's frescoes in the Collegiata of San Gimignano, both refered to by Meiss as being run of the mill of aesthetic creation after the Black Death. Ensuing grant has given occasion to feel qualms about Meiss' hypothesis in light of the fact that the previous work is currently accepted to have been created during the 1330s (Smart, 1978) and the last is presently dated before 1348 (Van Os, 1981, 240). We should likewise consider that "a portion of the characteristics most normal for late Trecento painting are as of now present, as Meiss himself was the first to perceive, in the frescoes by Taddeo Gaddi in the Baroncelli Chapel" (Smart, 1978, 108). As this church was painted amid the years 1328-34, it exhibits an early change in style which likewise undermines Meiss' postulation. The second component of the discussion concerns the adjustment in religious imagined that happened because of the demolition of the Black Death. Norman remarks on the prominence of altarpieces delineating Saint Sebastian and the clear relationship of his sufferings with those of the casualties of torment (Norman, 1995, I, 187-195), yet there is likewise a subtler change in style spoken to by the Strozzi Altarpiece (1357). Meiss contended that work of art regular of the mid fourteenth century harped on 'recognizable and all inclusive human experience' (Meiss, 1951, 28) and that it had been prevailing by a more noteworthy accentuation upon the various leveled and obstinate articulations of religious life, a rise of the congregation and a perplexity of the god. Giotto had spearheaded an aesthetic style that was set apart by its reasonable portrayal of three-dimensional space, agreeable utilization of shading and the making of a thoughtful reaction in the watcher. These highlights came to be normal for mid fourteenth painting, yet the Strozzi Altarpiece rejects the delineation of solid space, the figures 'float' and demonstrate an 'absence of correct spatial situation', the hues are 'incoherent and uneasy' and the artwork makes a separating feeling of wonder and riddle, which Cole depicts as 'abnormal', 'frightful', 'stern and unforgiving' and 'reserved' (Cole, 1976, 134-6). Meiss contended that this style was a cognizant come back to the Byzantine affected specialty of the earlier century (Meiss, 1951, 10) and that it is an impression of the religious accentuation upon blame and amends that was a response to the Black Death. We may likewise see an enthusiasm for the emblematic instead of practical portrayal of figures in the St John the Baptist Altarpiece (1370/80) by Giovanni del Biondo, where John stomps his adversary, Herod, underneath. John has the equivalent grim look and there is a similar feeling of mental withdrawal that has been seen even with Christ in the Strozzi Altarpiece. In any case, in Padua it is hard to find much proof for the dismissal of 'authenticity' in masterful style amid the second piece of the century. Altichiero's beautification of Lupi's funerary church in the Santo, a long way from endeavoring to separate the watcher, utilizes space and shape to attract the observer. His utilization of scene helps us to remember Lorenzetti and his figures are plainly propelled by Giotto, particularly the ladies who accumulate close to the foot of the cross and grasp in a way reminiscent of Joachim and Anna and the holy messengers who have the substance and articulation of those we find in the Arena Chapel. The scale, extent and plan of this fresco propose that this scene is being played out just past the dividers of the congregation and that we are seeing it as if through the curves of a loggia. The hues are agreeable and repressed and there is an impression of proximity and reality. Altichiero's style is more created and point by point than prior works, however its basic expectation and soul owes much to his inheritance from the prior fourteenth century. In Siena we likewise discover more conflicting elucidations of the progressions that happened in the mid-century. Henk Van Os has portrayed the manner by which social changes following the Black Death prompted significant changes in support: the affluent world class lost quite a bit of their political influence and a class of nouveau riche jumped up who had less enthusiasm for creative appointing. A significant part of the craftsmanship ended up imitative and preservationist and was all the more frequently charged in the areas encompassing Siena. In the city itself, just the well off body of the Ospedale of Santa Maria della Scala, which had gotten numerous endowments from casualties of the Black Death, kept dispatching new altarpieces, one of which, by Bartolommeo Bulgarini, incorporated the Assumption of the Virgin, a work of art which Van Os accepts to display "full, great figures, completely in the convention of Pietro Lorenzetti" (Van Os, 1981, 245). He contends that this composition does not hint at the level, progressive, magical plan which Meiss credited to it, however that it appears as a "plastically practical variant" of the Assumption thus remains inside the prior customs of Sienese painting (Van Os, 1981, 245). Unquestionably, the treatment of the Virgin and the utilization of expand gold impacts mirror the Sienese craftsmanship set up by Duccio and Simone Martini. Van Os reasons that progressions in imaginative generation after the Black Death were essentially because of various locales of support instead of changes in religious idea . The third part of the discussion concerns the subject of whether Meiss was on the whole correct to suggest that there was a solitary noteworthy move around 1348. Brilliant and Norman, for instance, contend that the Strozzi Altarpiece was not such a critical flight as Meiss had contended on the grounds that the point of reference for such a portrayal of Christ had been set in the Stefaneschi Altarpiece, painted by one of Giotto's partners and dated late 1320s – mid 1330s (Smart, 1978, 122 and Norman, 1995, I, 184). Albeit numerous pundits concur that the "center long periods of the fourteenth century can be depicted as a time of reassessment ever of painting" (Smart, 1978, 107), there are noteworthy contentions that that the development of imaginative style experienced various stages, not only one sudden change connected to the Black Death. John White talks about two expressive changes in the second 50% of the fourteenth century: the principal more traditionalist and less audacious and the second in which investigation and analysis again went to the fore (White, 1993, 542). Cole additionally contends that, and also the adjustment amidst the century, there was another adjustment in style around 1375 and "a reestablished enthusiasm for both the shape and substance of Giotto's craft" (Cole, 1976, 140). Plainly, since Meiss' unique hypothesis was proposed, much work has been finished by other workmanship students of history to challenge his thoughts. Despite the fact that the creation of workmanship in Florence in this period took on various structures from prior ones and the hypothesis this was because of the religious response incited by the Black Death can be given some assurance, there is less proof of this pattern in Padua and Siena. It is in this manner my decision that the center piece of the century saw a short set-back in creative undertaking, which was because of the obliteration caused by the Black Death, yet that the fourteenth century was for the most part a time of progressive advancements expanding on crafted by the before experts.>GET ANSWER