The document discusses exponential growth and decay models. Exponential growth models use the formula y = C(1 + r)t, where C is the initial amount, t is time, r is the growth rate, and (1 + r) is the growth factor. Exponential decay models use the formula y = C(1 - r)t, where (1 - r) is the decay factor and r is the decay rate. Examples are provided to demonstrate how to write, graph, and apply these models to problems involving compound interest, population growth, radioactive decay, and purchasing power.
This document reviews compound interest concepts, including how to calculate growth and decay factors from percentages and how to use the growth factor in an exponential growth formula. It provides an example of calculating the future value of $235 invested at 7.5% annual interest compounded yearly over 8 years, which equals $419.12.
This document provides a review of exponential growth and decay. It asks students to fill in blanks about exponential growth, with the correct answers being that the lower the base, the faster it grows. It then asks students to identify which function is decaying the fastest between y=(1/2)x and y=(3/4)x, with y=(1/2)x decaying the fastest. Finally, it asks which function is growing the fastest between y=4x, y=(1/2)x, and y=8x, with the highest base of y=8x growing the fastest.
The document discusses exponential growth and decay functions. Exponential growth functions have a base greater than 1, modeling an increasing pattern from small to big numbers over time. Exponential decay functions have a base between 0 and 1, modeling a decreasing pattern from big to small numbers. Examples are provided of functions modeling exponential growth and decay, along with explanations of how to determine which type of function based on the base.
This document contains lecture notes on exponential growth and decay from a Calculus I class at New York University. It begins with announcements about an upcoming review session, office hours, and midterm exam. It then outlines the topics to be covered, including the differential equation y=ky, modeling population growth, radioactive decay including carbon-14 dating, Newton's law of cooling, and continuously compounded interest. Examples are provided of solving various differential equations representing exponential growth or decay. The document explains that many real-world situations exhibit exponential behavior due to proportional growth rates.
ClassDojo is a tool that helps teachers develop positive character traits in students. It allows teachers to give students feedback points on behaviors like participation, kindness, and focus. Teachers can customize which behaviors they want to encourage or improve. ClassDojo can be used on computers and mobile devices, and it enables teachers to share student progress with other teachers, parents, and students.
The document discusses exponential functions and their key characteristics:
- Exponential functions have a constant growth or decay factor, meaning the dependent variable is multiplied by a fixed amount for each unit change in the independent variable.
- When the growth factor is greater than 1, it represents exponential growth. When it is less than 1, it represents exponential decay.
- Exponential functions have several distinguishing graphical properties, including having no x-intercepts, a y-intercept of (0,1), and being either always increasing or always decreasing depending on the growth factor.
The document provides an overview of an algebra 1 class, including expectations, topics that will be covered, prerequisites, and vocabulary. It states that the class will cover the real number system, properties of real numbers, variables and expressions, the Cartesian coordinate system, linear equations and inequalities. It emphasizes that students should be proficient with fractions and know their multiplication tables.
Radical and Polynomial Review ODD ANSWERS.pdfLomasAlg1
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Este documento contiene las respuestas a una revisi坦n de polinomios totalmente radicales. Incluye respuestas a problemas que involucran polinomios lineales, binomiales, de grados superiores y t辿rminos m炭ltiples.
Radical and Polynomial Review ODD ANSWERS.pdfLomasAlg1
油
Este documento contiene las respuestas a una revisi坦n de polinomios totalmente radicales. Incluye respuestas a problemas que involucran polinomios lineales, binomiales, de grados superiores y t辿rminos m炭ltiples.
