1. Applied Calculus,4/E, Deborah Hughes-Hallett Copyright 2010 by John Wiley and Sons, All Rights Reserved Section 1.6 The Natural Logarithm

2. Applied Calculus,4/E, Deborah Hughes-Hallett Copyright 2010 by John Wiley and Sons, All Rights Reserved Figure 1.63: The natural logarithm function climbs very slowly.

3. Applied Calculus,4/E, Deborah Hughes-Hallett Copyright 2010 by John Wiley and Sons, All Rights Reserved

4. ConcepTest Section 1.6 Question 5 Converting the function P = 100(1.07) t to the form P = P 0 e kt gives (a) P = 100e 1.07t (b) P = 100e 0.07t (c) P = 100e 1.0677t (d) P = 100e 0.0677t (e) P = 100e 0.93t

5. ConcepTest Section 1.6 Question 6 Converting the function P = 750e 0.04t to the form P = P 0 a t gives (a) P = 750(1.04) t (b) P = 750(0.04) t (c) P = 750(1.0408) t (d) P = 750(0.0408) t (e) P = 750(0.96) t

6. ConcepTest Section 1.6 Question 8 The solution to 200 = 30e 0.15t is:

7. ConcepTest Section 1.6 Question 17 Solve for x if y = e + 2 x.

8. Applied Calculus,4/E, Deborah Hughes-Hallett Copyright 2010 by John Wiley and Sons, All Rights Reserved Section 1.7 Exponential Growth and Decay

9. Applied Calculus,4/E, Deborah Hughes-Hallett Copyright 2010 by John Wiley and Sons, All Rights Reserved For a growth rate of 8% compounded annually, what is the doubling time? For a growth rate of 8% compounded monthly, what is the doubling time? For a growth rate of 8% compounded continuously, what is the doubling time?

10. Applied Calculus,4/E, Deborah Hughes-Hallett Copyright 2010 by John Wiley and Sons, All Rights Reserved The half-life of nicotine in the blood is 2 hours. A person absorbs 0.4 mg of nicotine by smoking a cigarette. Fill in the following table with the amount of nicotine remaining in the blood after t hours. t (hours)0246810 Nicotine (mg)0.4 0.20.1 0.05 0.0250.0125 Estimate when the amount of nicotine is reduced to 0.04 mg. What is the decay rate?

11. ConcepTest Section 1.7 Question 10 Estimate the half-life for the exponential decay shown in Figure 1.9. Figure 1.9 3

12. By Wednesday … Complete 1.5-7 HW Complete Lab 01 Read 1.8 Applied Calculus,4/E, Deborah Hughes- Hallett Copyright 2010 by John Wiley and Sons, All Rights Reserved