(50 points)the rate of change of y with respect to t is 3 times the value of the quantity 2 less than y. find an equation for y, given that y = 212 when t = 0. you get: a.) y = 212 + 2b.) y = 210 - 2c.) y = 210 + 2d.) y = 212 - 2e.) y = 214 - 2

The answer is    ======interpreting this to create a differential equation: "the rate of change of y with respect to t"means dy/dt.it is equal to "3 times the value of the quantity 2 less than y"    it's a separable differential equation. move all y-terms together and move all t terms together.    integrate both sides of the equation    use initial condition that says when t = 0, y = 212:     therefore        solving for y, we can use the definition of the logarithm to change this logarithmic equation into its equivalent exponential form, i.e.          thus    note that the initial condition of y(0) = 212 is only satisfied for  , so that is the answer. disregard the negative coefficient case.