Question

A medical researcher determines that t

t hours from the time a toxin is introduced 1

bacterial colony, the population will be

P(t)=9000(5+16e^−0.05t+te^−0.05t)

When does the maximum bacterial population occur? What is the maximum

population?

11. A medical researcher determines that t hours from the time a toxin is introduced 1 bacterial colony, the population will be P(t) = 9000 (5 + 16e-0.050 +te-0.05t) When does the maximum bacterial population occur? What is the maximum population?

Answer 1

Solution: given that P(+) = 9000 (5 416 4-0.057 tte-80st) first find destrative of Pct), with rexpect to t. r' (t) = 9000 (-0.8 0.0 0.05 Le-o-ost) 9000 p-oost (-0. -0.8 +1 -0.051] ***{0-3-0.05] + e -0.052 9000 0-0.05% Now, put p(t)=0 9000 -0.057 (0.2 -0.057] = 0 0.2-0.052=0 T 0.05t= 0.2 2 t= 0.2 0.05 2 xto e 16x8 U t= 4 again, differentiate with xexpect to t p"(t)= 9000 e.o.ost (-0.05) + + (0.2 -0.054) 9000(-0.05) P" (2)/2=4 = – 450 0-02 t (o) p"(t)/2 - 4 = -4.50 -0.24