In our modern world, we are inundated and grapple with data daily. As mathematicians, we are often more comfortable discussing the behavior of functions presented analytically, in contrast with the data-driven or tabular presentations of functions ubiquitous in our culture. This paper introduces an entry-level course, Mathematical Modeling and Applied Calculus, for students who will most likely take only one calculus-level course in college and who often have a weak algebraic background that suggests they would most likely not be successful in a traditional calculus course. During the first half of the course, students review precalculus ideas while learning techniques for identifying elementary functional models whose graphs correspond to the underlying shapes of data sets, refining their models in response to new data, and using the method of least squares to find "best possible" models of a given type. During the second half of the course, these functional models are analyzed using the tools of calculus. Mathematical Modeling and Applied Calculus focuses on real-life contexts and data sets, uses RStudio to study large data sets, and explores big picture conceptual understandings in order to develop the insights and skills needed to describe, model, and analyze many aspects of our world.