Intermediate Algebra – Student Workbook – Second Edition 2013

More documents

Recommendations

Info

$Lesson 2a – Assessment - Scottsdale Community College - Math Blog$

Lesson 3a – Introduction to Exponential Functions Mini-Lesson Writing Exponential Equations/Functions Given a set of data that can be modeled using an exponential equation, use the steps below to determine the particulars of the equation: 1. Identify the initial value. This is the a part of the exponential equation y = ab x . To find a, look for the starting value of the data set (the output that goes with input 0). 2. Identify the common ratio, b, value. To do this, make a fraction of two consecutive outputs (as long as the inputs are separated by exactly 1). We write this as the fraction y 2 y 1 to indicate that we put the second y on top and the first on the bottom. Simplify this fraction and round as the problem indicates to obtain the value of b. 3. Plug in the values of a and b into y = ab x to write the exponential equation. 4. Replace y with appropriate notation as needed to identify a requested exponential FUNCTION. Problem 14 MEDIA EXAMPLE – WRITING EXPONENTIAL EQUATIONS/FUNCTIONS The growth of the population of a small city is shown in the following table: Year Population 2000 12,545 2001 15269 2002 18584 Assume this growth is exponential. Let t = 0 represent the year 2000 and let a equal the initial population in 2000. Let b equal the ratio in population between the years 2001 and 2000. a) Write the equation of the exponential mathematical model for this situation. Round any decimals to two places. Be sure your final result uses proper function notation. b) Using this model, forecast the population in 2008 (to the nearest person). c) Also using this model, determine the nearest whole year in which the population will reach 50,000. Scottsdale Community College Page 110 Intermediate Algebra
Lesson 3a – Introduction to Exponential Functions Mini-Lesson GUIDELINES FOR SELECTING WINDOW VALUES FOR INTERSECTIONS While the steps for using the INTERSECTION method are straightforward, choosing values for your window are not always easy. Here are some guidelines for choosing the edges of your window: First and foremost, the intersection of the equations MUST appear clearly in the window you select. Try to avoid intersections that appear just on the window’s edges, as these are hard to see and your calculator will often not process them correctly. Second, you want to be sure that other important parts of the graphs appear (i.e. where the graph or graphs cross the y-axis or the x-axis). When choosing values for x, start with the standard XMin = -10 and Xmax = 10 UNLESS the problem is a real-world problem. In that case, start with Xmin=0 as negative values for a world problem are usually not important. If the values for Xmax need to be increased, choose 25, then 50, then 100 until the intersection of graphs is visible. When choosing values for y, start with Ymin = 0 negative values of Y are needed for some reason. For Ymax, all equations I am working with need to appear. So, if solving something like 234(1.23) x = 1000, then choose Ymax to be bigger than 1000 (say, 1500). If the intersection does not appear in the window, then try to change only one window setting at a time so you can clearly identify the effect of that change (i.e. make Xmax bigger OR change Ymax but not both at once). Try to think about the functions you are working with and what they look like and use a systematic approach to making changes. Problem 15 YOU TRY – WINDOW VALUES AND INTERSECTIONS In each situation below, you will need to graph to find the solution to the equation using the INTERSECTION method described in this lesson. Fill in the missing information for each situation. a) Solve 54(1.05) x =250 Y1=________ WINDOW Xmin=____, Xmax= ______ Y2 = _______ Ymin=____, Ymax= ______ Solution: x = ______________ Round to two decimals. b) Solve 2340(0.82) x = 1250 Y1=________ WINDOW Xmin=____, Xmax= ______ Y2 = _______ Ymin=____, Ymax= ______ Solution: x = ______________ Round to two decimals. c) Solve 45=250(1.045) x Y1=________ WINDOW Xmin=____, Xmax= ______ Y2 = _______ Ymin=____, Ymax= ______ Solution: x = ______________ Round to two decimals. Scottsdale Community College Page 111 Intermediate Algebra
Page 1 and 2:
Scottsdale Community College Interm
Page 3 and 4:
Table of Contents Lesson 1a - Intro
Page 5 and 6:
Lesson 1a - Introduction to Functio
Page 7 and 8:
Name: _____________________ Date: _
Page 9 and 10:
Page 11 and 12:
Page 13 and 14:
Page 15 and 16:
Page 17 and 18:
Page 19 and 20:
Page 21 and 22:
Name: _____________________ Date: _
Page 23 and 24:
Page 25 and 26:
Page 27 and 28:
Page 29 and 30:
Name: _____________________ Date: _
Page 31 and 32:
Lesson 1b - Linear Equations In the
Page 33 and 34:
Name: _____________________ Date: _
Page 35 and 36:
Lesson 1b - Linear Equations Mini-L
Page 37 and 38:
Page 39 and 40:
Page 41 and 42:
Page 43 and 44:
Page 45 and 46:
Name: _____________________ Date: _
Page 47 and 48:
Lesson 1b - Linear Equations Practi
Page 49 and 50:
Page 51 and 52:
Page 53 and 54:
Name: _____________________ Date: _
Page 55 and 56:
Lesson 2a - Linear Functions and Ap
Page 57 and 58:
Name: _____________________ Date: _
Page 59 and 60:
Page 61 and 62:
Page 63 and 64: Lesson 2a - Linear Functions and Ap
Page 69 and 70: Name: _____________________ Date: _
Page 77 and 78: Lesson 2b - Functions and Function
Page 99 and 100: Lesson 3a - Introduction to Exponen
Page 113: Lesson 3a - Introduction to Exponen
Page 125 and 126: Lesson 3b - More Exponential Functi
Page 147 and 148: Lesson 4a - Introduction to Logarit
Page 165 and 166:
Lesson 4b - More on Logarithms This
Page 167 and 168:
Name: _____________________ Date: _
Page 169 and 170:
Lesson 4b - More on Logarithms Mini
Page 171 and 172:
Page 173 and 174:
Page 175 and 176:
Page 177 and 178:
Name: _____________________ Date: _
Page 179 and 180:
Lesson 4b - More on Logarithms Prac
Page 181 and 182:
Page 183 and 184:
Page 185 and 186:
Name: _____________________ Date: _
Page 187 and 188:
Lesson 5a - Introduction to Quadrat
Page 189 and 190:
Name: _____________________ Date: _
Page 191 and 192:
Page 193 and 194:
Page 195 and 196:
Page 197 and 198:
Page 199 and 200:
Page 201 and 202:
Name: _____________________ Date: _
Page 203 and 204:
Page 205 and 206:
Page 207 and 208:
Page 209 and 210:
Name: _____________________ Date: _
Page 211 and 212:
Lesson 5b - Solving Quadratic Equat
Page 213 and 214:
Name: _____________________ Date: _
Page 215 and 216:
Page 217 and 218:
Page 219 and 220:
Page 221 and 222:
Page 223 and 224:
Page 225 and 226:
Page 227 and 228:
Page 229 and 230:
Page 231 and 232:
Name: _____________________ Date: _
Page 233 and 234:
Page 235 and 236:
Page 237 and 238:
Page 239 and 240:
Page 241 and 242:
Name: _____________________ Date: _
Page 243 and 244:
Lesson 6a - Exponents and Rational
Page 245 and 246:
Name: _____________________ Date: _
Page 247 and 248:
Page 249 and 250:
Page 251 and 252:
Page 253 and 254:
Page 255 and 256:
Page 257 and 258:
Name: _____________________ Date: _
Page 259 and 260:
Page 261 and 262:
Page 263 and 264:
Page 265 and 266:
Name: _____________________ Date: _
Page 267 and 268:
Lesson 6b - Rational Exponents & Ra
Page 269 and 270:
Name: _____________________ Date: _
Page 271 and 272:
Lesson 6b - Rational Exponents and
Page 273 and 274:
Page 275 and 276:
Page 277 and 278:
Page 279 and 280:
Name: _____________________ Date: _
Page 281 and 282:
Page 283 and 284:
Page 285 and 286:
Name: _____________________ Date: _
Page 287 and 288:
Appendix A: You Try Answers Lesson
Page 289 and 290:
Appendix A: You Try Answers You Try
Page 291 and 292:
Page 293 and 294:
show all

Intermediate Algebra – Student Workbook – Second Edition 2013

You also want an ePaper? Increase the reach of your titles

Delete template?

Save as template?