A bacteria culture has population with

MATHEMATICS · Single correct · AP · Calculus AB · Differential Equations · Differential Equations

Problem

A bacteria culture has population N(t)N(t) with N(0)=500N(0)=500. For 0≤t<40\le t<4 hours, dNdt=0.3N\dfrac{dN}{dt}=0.3N. For 4≤t≤104\le t\le10 hours, the growth constant changes so that dNdt=k2N\dfrac{dN}{dt}=k_2N. If N(10)=4000N(10)=4000, what is the value of k2k_2 (in h−1^{-1})? (a) 0.25 h−10.25\,\text{h}^{-1} (b) 0.15 h−10.15\,\text{h}^{-1} (c) 0.10 h−10.10\,\text{h}^{-1} (d) 0.21 h−10.21\,\text{h}^{-1}

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