MATH-S 343 Chapter Notes - Chapter 1: Asymptote, Cell Growth, Partial Differential Equation
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S343 section 1. 1 notes- types of differential equations; exponential growth/decay. Exponential growth and decay mice present to start with horizontal slope (asymptote) occurs when 900 mice present match) present positive slope (population increases) when more than 900 mice the cell grows. Its rate of growth is proportional to its surface area, and assume it is spherical: rate of change- proportio(cid:374)al to a(cid:373)ou(cid:374)t of (cid:862)stuff(cid:863, ex. Assume owls eat mice at rate of 15 mice/day. 450 comes from 15 mice/day multiplied by assumed 30 days in a month (made units of rates. Let (cid:4666)(cid:1872)(cid:4667)= number of mice at time (cid:1872) Rate of change of mouse population is (cid:3040)(cid:3047)=(cid:882). (cid:887) (cid:886)(cid:887)(cid:882) (cid:882). (cid:887)(cid:4666)(cid:887)(cid:882)(cid:882)(cid:4667) (cid:886)(cid:887)(cid:882)= (cid:884)(cid:882)(cid:882) very negative slope (population goes down) when less than 900. Let (cid:4666)(cid:1872)(cid:4667) be the weight of a cell at time (cid:1872). Write a differential equation that gives a model to how. Relates weight to sa; assume density constant, so weight (cid:4666)(cid:1872)(cid:4667) should be proportional to volume.
