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1* A new East'food firm predicts that the number of franchises for its products will grow at the rate Eff = 36\" + 1] 1ft\"! 1 where t is the number of veers. If there is one franchise [n=1) at present [t=] . how many franchise. are predicted for T years from now?(5 Marks] 2* Estimate the denite integral using Simpson's Rule with a = 4. Round all calculations to three decimal places. [5 Marl-ts) 1: 1+2: 3. Let y) he the size of a colony of bacteria after t hours. Suppose the rate of growth of the colony is equal to eight times the nnohalf power of its present size. Solve the dierential equatiun which models this growth and an initial condition that says that at time zero the colony is of size Inn. {5 Marks} 4- Solve each differential equation and initial condition. {15 Marks] A.yr='/e*~, y[]=l B. y' = 3;\". 3,112} = 1. C. y! + 4;: =15e=, yw) = a