A laboratory tracks the number of bacteria in a culture and the amount of a nutrient…
MATHEMATICS · Multi-part · AP · AP Precalculus · Exponential and Logarithmic Functions · Exponential and Logarithmic Functions
Problem
A laboratory tracks the number of bacteria in a culture and the amount of a nutrient in the same solution over time t (in hours). The bacteria count is modelled by B(t)=200⋅2t, while the quantity of nutrient (in milligrams) remaining is given by N(t)=5000−50t2 for 0≤t≤10.
(i) Calculate B(2) and N(2).
(ii) Determine, correct to the nearest integer hour, the time when the bacteria count first exceeds the amount of nutrient remaining. Show how you arrive at your answer.
(iii) Give a clear argument to state which of B(t) or N(t) will be greater for all times after the hour obtained in part (ii), provided the expressions remain defined within 0≤t≤10.