A stock went on the market and began with a start value of $2. After 6 months of being on the market it reached its maximum value of 52$ but then dropped back down to 2$ by the 12th month. Three competing investment firms have come up with the following models.

Royal Bank: p(t) = 25/648 (t)2 (t-12)2+2

TD Investment: p(t) = -25 cos⁡(pi/6 (t))+27

JerCO UltraSmart: p(t)= 50/log(7) ∙
log⁡(t+1)+27

So my remaining questions given that info are.

1.For each case determine the intervals of time that would be good to buy the stock and the intervals or points that would be good to sell over the first 3 years on the market.

2.At an economics conference the stockbroker's investment subcommittee decides that Royal Bank's quartic function is good for short term and that JerCo UltraSmart's Is good for the long term. At what time value for "t" should they switch from the quartic to the logarithmic function?

3.The macro economics committee also looked at the data were convinced the stock data could be modelled by a cubic function. Show any and all calculations to determine a cubic function necessary shifts, stretches, or compressions.

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