MATHEMATICS · Multi-part · AP · Calculus AB · Differential Equations · Differential Equations
Problem
Two competing strains of bacteria, A and B, are placed in identical nutrient solutions. Strain A obeys dtdA=0.62A with initial population A(0)=3×103 cells. Strain B obeys dtdB=0.48B with initial population B(0)=9×103 cells.
(a) Obtain explicit formulas for A(t) and B(t), where t is measured in hours.
(b) Determine the exact time at which the two strains have equal populations. Express your answer in hours.
(c) For t greater than the time found in part (b), identify which strain will dominate the culture. Justify your answer mathematically.
(d) Calculate how many cells of the dominant strain are present exactly 5 hours after the populations become equal. Express your answer to the nearest hundred cells.