PPT-Linear Vs. Exponential Growth

Differentiate between linear and exponential functions 4 3 2 1 0 In addition to level 3 students make connections to other content areas andor contextual situations outside of math   Students will construct compare and interpret linear and exponential function models and solve problems in context with each model. e Ax where is vector is a linear function of ie By where is then is a linear function of and By BA so matrix multiplication corresponds to composition of linear functions ie linear functions of linear functions of some variables Linear Equations . the. Problem. (MAVT). Y. İlker TOPCU. , . Ph. .D.. www.ilkertopcu.. net www.. ilkertopcu. .org www.. ilkertopcu. .. info. www.. facebook. .com/. yitopcu. twitter. .com/. yitopcu. . MAVT vs. MAUT . Exponential Growth Functions. If a quantity increases by the same proportion . r. in each unit of time, then the quantity displays exponential growth and can be modeled by the . equation. Where. C = initial amount. (4.1) Exponential & Logarithmic Functions in Biology. (4.2) Exponential & Logarithmic Functions: Review. (4.3) . Allometry. (4.4) Rescaling data: Log-Log & Semi-Log Graphs. Recall from last time that we were able to come up with a “best” linear fit for . Chapter 10. Re-Expressing data:. Get it Straight. Objectives:. Re-expression of data. Ladder of powers. Straight to the Point. We cannot use a linear model unless the relationship between the two variables is linear. Often . Evaluating Rational & Irrational Exponents. Graphing Exponential Functions . f(x) = a. x. Equations with . x. and . y. Interchanged. Applications of Exponential Functions. Use calculators to calculate graphing points. Date: ______________. Warm-Up. Rewrite each percent as a decimal.. 1.) 8% 2.) 2.4% 3.) 0.01%. 0.08 0.024 0.0001. Evaluate each expression for x = 3.. 4.) 2. x. 5.) 50(3). x. 6.) 2. $6500 principle earning 2.8% compounding monthly after 2 years. $2000 principle earning 5.4% compounding semiannually after 4 years. Exponential Growth & Decay . Standard Form:. y = a•b. x. However, depending on the question, we have to change the growth factor. . Exponential Growth. Exponential growth. occurs when an quantity increases by the same rate . r. in each period . t. . When this happens, the value of the quantity at any given time can be calculated as a function of the rate and the original amount. . Differentiate between linear and exponential functions.. 4. 3. 2. 1. 0. In addition to level 3, students make connections to other content areas and/or contextual situations outside of math..  . Students will construct, compare, and interpret linear and exponential function models and solve problems in context with each model.. molecular dynamics systems of coupled harmonic oscillators n = 2 or 3 n �� 1 continuum exponential growth and decay molecular dynamics systems of coupled harmonic oscillators Growth of Product . U. sing Polymerase Chain Reaction (PCR). Intro. Using math to solve a biological science problem. Students will use their knowledge of:. Exponential equations. Molecular biology. HS Biology Standards. GROWTH. Growth. defined as the increase in size of an organism or of its parts due to the synthesis of . Protoplasm. (includes both cytoplasm and nucleus) or . Apoplasmatic. substances . (substance produced by cells and forms a part of the tissues . All slides in this presentations are based on the book Functions, Data and Models, S.P. Gordon and F. S Gordon. ISBN 978-0-88385-767-0. Fitting Data to An Exponential Function. Although Linear Regression is a powerful tool, not all relationships between two quantities are linear. (See scatterplots in figure 5.28).