Question #16797

You work for the Department of Pathology where you study the growth of a microbial culture of Escherichia coli under very special conditions. The number of bacteria at time t [in hours] can be estimated by
f(t) = (t + 1) e^[√(t+2)]
Use logarithmic differentiation in order to determine the relative growth rate at time t = 3 and give your result in percent growth per hour.

Expert's answer

Logarithmic differentiation: f'(t)=f(t)ln(f(t))]'

f'(t)=(t + 1) e^[√(t+2)](1/(t+1))(1+(t+1)/2√(2+t))

f'(t)=e^[√(t+2)](1+(t+1)/2[√(t+2)])

f'(3)=e^√5(1+4/2√5)=17.73

f'(t)=(t + 1) e^[√(t+2)](1/(t+1))(1+(t+1)/2√(2+t))

f'(t)=e^[√(t+2)](1+(t+1)/2[√(t+2)])

f'(3)=e^√5(1+4/2√5)=17.73

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