Lesson 13 - Logs and Exponential - Pg. 157: 10,13,,28,31,39,40

Lesson 13 - Logs and Exponential - Pg. 157: 10,13,,28,31,39,40

Lesson 13 - 4.2 # 10 - Convert between exponential forms:

Convert

Ans.: a = 4, and k = ln(8^1.3) = 2.7033

So

Lesson 13 - 4.2 # 13 - Convert between exponential forms:

Convert

Ans.: a = 0.3, and b = e^0.7 = 2.0138

So

Lesson 13 - 4.2 # 28 - Solve and give an exact solution if there is one for .

Group like terms:

take ln of both sides

Lesson 13 - 4.2 # 31 - Exponential Tripling given (0, 3) and (3, 100), where t is hr. and N is number of bacteria.

So exp. inc. fct:

Then

(a) Formula is

(b)

Solve for t:

Lesson 13 - 4.2 # 39 - Study of Exponential decay given ½ life of C-14 has 5728 years and 100 - 46 = 54% remaining in 1991.

Find when was 100%

First find rate of decay or b

For ½ life:

So

Then t for problem is found by solving for t in

So since it took about 5092 to decay from 100% to 54 percent, then the man died about 5092 years ago or 1991 - 5092 = 3101 BCE
Lesson 13 - 4.2 # 40 - Study of Exponential growth or inflation: 40% over 5-years period.

(a) Find rate of change year or r from:

1+r = 1.0696104 or r = 0.0696104 or

Rate is 6.0961 %

(b) How long does it take for price to rise by 5%? Find t when:

then t is

(c) Convert

So continuous rate formula is