Answer to Question #17058 in Calculus for Cherry

Question

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.

Answer 1

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