MATHEMATICS · Single correct · AP · Calculus BC · Differential Equations · Differential Equations
Problem
A bacterial culture grows according to dtdp=0.05p, where p(t) is the number of bacteria and t is measured in hours. Starting with p(0)=1000, a student makes three successive tangent-line steps with constant step size 2 hours to approximate p(6). The student obtains the value 1331. Which statement BEST interprets this numerical result in context?
(a) After 6 hours the culture’s growth rate is predicted to be about 1331 bacteria per hour.
(b) The approximation suggests the population will increase by approximately 1331 bacteria over the 6-hour interval.
(c) After 6 hours the culture is predicted to contain approximately 1331 bacteria.
(d) Because 1331 exceeds the initial 1000 bacteria, the model predicts a total of about 2331 bacteria after 6 hours.