<p>P.o.D.-Solve each logarithmic equation ALGEBRAICALLY to three decimal places. 1.) ln(4x)=1 2.) 2-6 ln(x)=10 3.) 4.) </p><p>1.) 0.6796</p><p>2.) 0.2636</p><p>3.) 5.39</p><p>4.) 9 3.5 – Exponential and Logarithmic Models *Memorize the five most common types of mathematical models involving exponential and logarithmic functions (pg.257) 1. Exponential growth model: 2. Exponential decay model: 3. Gaussian model(bell shaped): 4. Logistic growth model(stretched S): 5. Logarithmic models(upside down hockey stick) *Memorize the shapes of these graphs (Fig. 3.29) on page 257. EX: The population P of a city is given by , where t=0 represents 1996. According to this model, when did the population reach 150,000?</p><p>Since 1996 is t=0, 8 years later would be 2004. Exponential Growth: EX: In a research experiment, a population of fruit flies is increasing according to the law of exponential growth. After 2 days there are 125 flies, and after 4 days there are 350 flies. How many flies will there be after 6 days? Substitute what we know into the equation(s).</p><p>Now solve one of the two equations for a.</p><p>Next, substitute this into the other equation and solve for b. Use this to find a. Finally, substitute everything back into the equation for exponential growth.</p><p>About 980 fruit flies. Carbon Dating Model:</p><p>EX: Estimate the age of a newly discovered fossil in which the ratio of carbon 14 to carbon 12 is . Substitute. Gaussian Models (Carl Gauss): 1.</p><p>2. Used with “normally” distributed data</p><p>3. Will be a bell shaped curve</p><p>4. The average value of a population will occur at the maximum of the function. Side Note: A standard normal distribution fits the model . EX: Last year, the math scores for students in a particular math class roughly followed the normal distribution given by , 30<x<110 where x is the math score. Sketch the graph of this function, and use it to estimate the average math score.</p><p>The average score for students in the math class was 74. EX: On a college campus of 7500 students, one student returns from vacation with a contagious and long- lasting virus. The spread of the virus is modeled by where y is the total number of students affected after t days. The college will cancel classes when 30% or more of the students are affected. How many students will be infected after 4 days?</p><p>After how many days will the college cancel classes? 30% of 7500 is 2250. Graph the equation and y=2250</p><p> about 9 days EX: On the Richter scale, the magnitude R of an earthquake of intensity I is given by , where is the minimum intensity used for comparison. Find the magnitude R of an earthquake of intensity I. </p><p> a. I=68,400,000</p><p> b. I=42,275,000 a.</p><p> b. R=log(42275000)=7.626 Upon completion of this lesson, you should be able to:</p><p>1. Identify the different types of exponential models by their equation and graph.</p><p>2. Solve story problems involving the different exponential models. For more information, visit http://academics.utep.edu/Portals/1788/CALCULUS %20MATERIAL/3_5%20EXPO%20AND%20LOG %20MODELS.pdf </p><p>HW Pg.264 3-30 3rds, 40, 43, 63, 73- 78 Quiz 3.3-3.5 tomorrow</p>