Exponential growth solutions [eqns (23) to (35)] in constant conditions. Light flux density, I₀, and hence parameter β [eqn (8)], are varied from near zero to 500 J (PAR) m⁻² s⁻¹ (2300 µmol PAR m⁻² s⁻¹). Two values of parameter k_S are applied. Specific gross photosynthetic rate π_g is given by eqn (33). The vertical dashed line labelled μ = 0 marks the π_g value for zero specific growth rate, μ = 0, for k_S = 1 d⁻¹ (the value is slightly different for k_S = 5 d⁻¹) [eqns (33), (30), (27)]. (A) Specific growth rate μ, eqns (27); (B) specific respiration rate ρ, eqns (14), (27); (C) respiration:gross photosynthesis ratio r_R:Pg, eqns (21), (13), (8), (27); (D) substrate fraction C_S, eqn (27), (8); (E, F) slopes of graphs in (A) and (B), respectively, were calculated numerically.