MATHEMATICS · Multi-part · AP · AP Precalculus · Exponential and Logarithmic Functions · Exponential and Logarithmic Functions
Problem
Two species of algae, species A and species B, are introduced simultaneously into identical nutrient solutions. Their masses (in milligrams) are modeled for t≥0 days by
A(t)=600e0.020t,B(t)=300e0.050t.
Assume the models remain valid for at least the first 100 days.
(a) Describe the practical meanings of the numerical coefficients 600,300,0.020, and 0.050 in the context of the experiment.
(b) Without explicitly solving for t, explain why there must be a positive time at which the masses of the two species are equal.
(c) Without using algebraic manipulation of the formulas, determine which species has the greater mass after 100 days. Justify your answer in terms of growth behavior.