This math unit navigates through the profound understanding and application of exponential functions, starting with conceptual comprehension and progressing towards intricate problem solving. Students first delve into the basics of exponential functions, learning to identify components such as initial values, rates of change, and specific terms within decay and growth scenarios in both discrete and continuous contexts. Initial topics focus on linking real-world scenarios like population dynamics and financial growth with exponential decay and growth functions. As the unit progresses, students enhance their skills by applying these concepts to solve for unknown variables such as time, rates, and initial amounts. They are required to manipulate equations to find specific details like the time required for a population to reach a certain size or the rate at which a toxin's concentration declines. This involves a deep dive into logarithmic calculations, emphasizing the use of logarithms to isolate and solve variables in both growth and decay formulas. Towards the end of the unit, the focus shifts slightly to logarithmic scales, where students apply their skills to calculate magnitudes using logarithmic values in real-world measures like earthquakes and sound levels. This seamless progression from basic identification to complex problem-solving showcases a comprehensive exploration of exponential and logarithmic functions within real and varied contexts.Skills you will learn include:
Topics are small, focused areas which build towards the greater unit's goals.