A bacteria population is modeled by

MATHEMATICS · Single correct · A Level · Mathematics · Differentiation · Differentiation

Problem

A bacteria population P(t)P(t) is modeled by dPdt=k (1200−P)\dfrac{dP}{dt}=k\,(1200-P), where tt is measured in hours. At the instant when the population is 400 bacteria, it is increasing at a rate of 60 bacteria per hour. What is the value of the constant kk? (a) 0.15 hr−10.15\,\text{hr}^{-1} (b) 0.075 hr−10.075\,\text{hr}^{-1} (c) 0.05 hr−10.05\,\text{hr}^{-1} (d) 13.3 hr−113.3\,\text{hr}^{-1}

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