ab calculus ap multiple choice questions

If the initial value y(0) > a, the population will decrease over time until it levels out to y = a, and if y(0) < a, then it will increase until it reaches y = a. The carrying capacity is a big deal for a couple of reasons. One solution is y = 0, and the other solution is y = carrying capacity. The equation might not always appear in this form, so to find the carrying capacity, set the equation equal to 0 and solve for y.

In this equation, k and a are constants, and a is the carrying capacity. The differential equation for logistic growth is this guy right here. In words, the logistic growth formula says, 'The rate of change of a population is jointly proportional to the size of the population and the difference between the population and the carrying capacity.'

The model is called logistic growth, and it takes the form of a differential equation.

There's a model that accounts for the fact that resources and space are not infinite and that a population has a 'carrying capacity' that it can't exceed in the long run. If a population of bacteria kept growing exponentially, the world would be overrun with bacteria pretty quickly. extra help with the stuff that only shows up on the Calculus BC exam, like parametric and polar equations, logistic growth, and two dudes named Taylor and Maclaurin.Įxponential growth is a nice model to work with mathematically (well, nice-ish), but its big flaw is that it's not completely realistic.a complete walkthrough of every single subject that's likely to show up on the exam, broken down into bite-sized chunks by topic-we're talking limits, derivatives, integrals, and more.answer explanations to figure out where you went wrong…or right.two full-length practice exams that are just like the real thing.a diagnostic exam to measure where you are.Inside Shmoop's guide to the AP Calculus BC exam, you'll find Our Test Prep resources will help you prepare for exams with fun, engaging, and relatable materials that bring the test to life. Shmoop is a labor of love from folks who love to teach. What's Inside Shmoop's Online AP Calculus BC Test Prep Looking for AP Calculus AB? We got you for that too.

You're in the big leagues now with Calculus BC, but don't worry-we've got your back. why polar curves are about more than a sassy polar bear reclining on an ice shelf.how to keep from bursting into tears during the free response section.what the AP exam is all about, how it's scored, and why guessing can be a good thing.If you're feeling a little blue about derivatives, infinite series, and things that rhyme with shmalculus, check out the Shmoop guide to AP Calculus BC for all your calculating needs.

Ab calculus ap multiple choice questions