October 28, 2009 - Ottawa Hills Local School District · 2017-10-04 · October 28, 2009 Newton's...

12
October 28, 2009

Transcript of October 28, 2009 - Ottawa Hills Local School District · 2017-10-04 · October 28, 2009 Newton's...

Page 1: October 28, 2009 - Ottawa Hills Local School District · 2017-10-04 · October 28, 2009 Newton's Law of Cooling T(t) = Tm + (To - Tm)e-kt T = temperature t = time T m = temperature

October 28, 2009

Page 2: October 28, 2009 - Ottawa Hills Local School District · 2017-10-04 · October 28, 2009 Newton's Law of Cooling T(t) = Tm + (To - Tm)e-kt T = temperature t = time T m = temperature

October 28, 2009

Page 3: October 28, 2009 - Ottawa Hills Local School District · 2017-10-04 · October 28, 2009 Newton's Law of Cooling T(t) = Tm + (To - Tm)e-kt T = temperature t = time T m = temperature

October 28, 2009

3.5 Solving Exponential and Logarithmic Equationsx=3

42764

Page 4: October 28, 2009 - Ottawa Hills Local School District · 2017-10-04 · October 28, 2009 Newton's Law of Cooling T(t) = Tm + (To - Tm)e-kt T = temperature t = time T m = temperature

October 28, 2009

4 log10(x-6) = 11

Page 5: October 28, 2009 - Ottawa Hills Local School District · 2017-10-04 · October 28, 2009 Newton's Law of Cooling T(t) = Tm + (To - Tm)e-kt T = temperature t = time T m = temperature

October 28, 2009

4. log3x + log3(x2-8) = log38x

Page 6: October 28, 2009 - Ottawa Hills Local School District · 2017-10-04 · October 28, 2009 Newton's Law of Cooling T(t) = Tm + (To - Tm)e-kt T = temperature t = time T m = temperature

October 28, 2009

3 ln x = 5

Page 7: October 28, 2009 - Ottawa Hills Local School District · 2017-10-04 · October 28, 2009 Newton's Law of Cooling T(t) = Tm + (To - Tm)e-kt T = temperature t = time T m = temperature

October 28, 2009

log (x-4) = 1

Page 8: October 28, 2009 - Ottawa Hills Local School District · 2017-10-04 · October 28, 2009 Newton's Law of Cooling T(t) = Tm + (To - Tm)e-kt T = temperature t = time T m = temperature

October 28, 2009

7 - 3e-x = 2

Page 9: October 28, 2009 - Ottawa Hills Local School District · 2017-10-04 · October 28, 2009 Newton's Law of Cooling T(t) = Tm + (To - Tm)e-kt T = temperature t = time T m = temperature

October 28, 2009

2x + 2-x

2= 3

Page 10: October 28, 2009 - Ottawa Hills Local School District · 2017-10-04 · October 28, 2009 Newton's Law of Cooling T(t) = Tm + (To - Tm)e-kt T = temperature t = time T m = temperature

October 28, 2009

Order of Magnitude: The difference in the common logs of two distances. Its a way to compare like quantities.

ex.

1. A dollar is 2 orders of magnitude greater than a penny.

Find the order of magnitude of a bird weighing 20g and a hen weighing 2 kg.

Page 11: October 28, 2009 - Ottawa Hills Local School District · 2017-10-04 · October 28, 2009 Newton's Law of Cooling T(t) = Tm + (To - Tm)e-kt T = temperature t = time T m = temperature

October 28, 2009

Earthquake Intensity

R = log + Ba1T

How many more times severe was the 1995 Kobe, Japan earthquake (R = 7.2) than the 1994 Los Angeles earthquake (R = 6.6)

Page 12: October 28, 2009 - Ottawa Hills Local School District · 2017-10-04 · October 28, 2009 Newton's Law of Cooling T(t) = Tm + (To - Tm)e-kt T = temperature t = time T m = temperature

October 28, 2009

Newton's Law of Cooling

T(t) = Tm + (To - Tm)e-kt

T = temperaturet = time

Tm = temperature of surrounding medium

To = initial temperature of the object

A cake is removed from an oven at 350oF and cools to 120oF

after 20 min in a room at 65oF. How long will the cake take to

cool to 90oF?