Suppose N(t) denotes a population size at time t where the dN/dt = 0.02N(t). If the population size at time t = 4 is equal to 100, use a linear approximation to estimate the size of the population at time t = 4.1. L(4.1) =
Added by Summer R.
Close
Step 1
02N(t) \), which describes the rate of change of a population, \( N \), with respect to time, \( t \). This equation suggests that the population grows at a rate proportional to its current size. Show more…
Show all steps
Your feedback will help us improve your experience
Suman Saurav Thakur and 77 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
Eduard S.
Suppose that a population, whose size at time t is denoted by N(t), grows according to dN/dt = 0.3N with N(0) = 20. Solve this differential equation and find the size of the population at time t = 5.
Madhur L.
Suppose a population $ P(t) $ satisfies $ \frac {dP}{dt} = 0.4 P - 0.001P^2 P(0) = 50 $ where $ t $ us measured in years. (a) What is the carrying capacity? (b) What is $ P'(0)? $ (c) When will the population reach $ 50% $ of the carrying capacity?
Differential Equations
Models for Population Growth
Recommended Textbooks
Calculus: Early Transcendentals
Thomas Calculus
Transcript
Watch the video solution with this free unlock.
EMAIL
PASSWORD