2. A biologist models the effect of introducing a toxin to a bacteria colony by given the function for the first 10 hours as B(t) = (2t + 1) / (t^2 + t + 6.5) where B(t) is the approximate population of the colony (in millions of bacteria) t hours after the toxin was introduced. a) What is the practical domain? b) At what time does the bacteria colony reach their maximum population, and what is this maximum population? Verify appropriately that this value is the maximum.
Added by Jose Miguel J.
Close
Step 1
Use the function to model the effect of introducing toxin t0 bacteria colony by given Ihe function for the first 10 hours as 2t + 1 R(t) = 04t+65. Show more…
Show all steps
Your feedback will help us improve your experience
Madhur L and 95 other Calculus 1 / AB educators are ready to help you.
Ask a new question
Labs
Want to see this concept in action?
Explore this concept interactively to see how it behaves as you change inputs.
Key Concepts
Recommended Videos
Bacteria Population Assume that the number of bacteria $R(t)$ (in millions) present in a certain culture at time $t$ (in hours) is given by $$R(t)=t^{2}(t-18)+96 t+1000 \text { . }$$ a. At what time before 8 hours will the population be maximized? b. Find the maximum population.
Graphs and the Derivative
Higher Derivatives, Concavity, and the Second Derivative Test
A bacterial colony is estimated to have a population of P(t) = 24t + 10 million 0+1 hours after the introduction of a toxin. What is the rate of change of the population 1 hour after the toxin is introduced (at t = 1)? Is the population increasing or decreasing at that time?
Madhur L.
Assume that the number of bacteria R(t) (in millions) present in a certain culture at time t (in hours) is given by R(t) = t^2(t - 18) + 96t + 2000. a. At what time before 8 hours will the population be maximized? b. Find the maximum population. a. The population will be maximized at t = hours. b. The maximum population is million bacteria.
Recommended Textbooks
Calculus: Early Transcendentals
Thomas Calculus
Transcript
Watch the video solution with this free unlock.
EMAIL
PASSWORD