Question

y (15 pts) Un a frosty Halloween eve, the temperature starts dropping faster and faster. As a result, the trick-or-treaters leave the streets at an exponential rate. The decay constant modeling this trick-or-treat exodus is -3. Time is in minutes, and there are 1,000 trick-or-treaters to begin with. (You do not need to simplify your answers!) a) What is the general equation for C(t), the number of children on the street after t minutes? (That is, c(t) = ?) b) What is the general differential equation that fits this scenario? (That is, C'(t) = ?) c) How long does it take for the population to decrease by half? (What is the "half-life" of the trick-or-treaters?) (Units!) d) How many trick-or-treaters are there after 20 minutes? e) What is the exodus rate of trick-or-treaters when there are 20 of them left on the street? (Units!)

Answer 1

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tGenoral eguabon c )e- 2t Ct General dhiffrunbial eguabion dt decay cons tent O693 Ce) t2