If C (in units of 10⁻⁴ molar) is the concentration of glucose in a solution, then E. coli bacteria in the solution grow at a rate, R (in cell divisions per hour), given by

(a) Find the growth rate of bacteria growing in 2⋅10⁻⁴ molar glucose solution. Include units.
(b) Find dR∕dC.
(c) Find dR∕dC|_C=2. Include units.
(d) Find the tangent line approximation of the growth rate for bacteria growing in glucose concentrations near 2 ⋅ 10⁻⁴ molar.

(e) Use the tangent line approximation to estimate the growth rate in a 2.2 ⋅ 10⁻⁴ molar glucose solution. Compare it with the growth rate from the original model.

Transcribed Image Text:

R = 1.35C 0.22 + C cell divisions per hour.