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NEWS• Still pondering what to do with the test• Quiz will be a TAKE-HOME (due Wednesday)

• Wednesday at lunch I will be going over the test (we have class right before)


TAKE HOME QUIZ1. Worksheet #1c ON WEBSITE if you lost it

2. Worksheet #3

3. Workbook p.159 #2e4. Workbook p.160 #3d (SHOW YOUR WORK OR YOU GET ZERO!!)

5. Workbook p.174 #3b

6. Workbook p.176 #7e

7. Workbook p. 176 #8f

8. Workbook p. 177 #12b

9. Workbook p.177 #14c

10. Workbook p.179 #25b


Let’s go over a log question…p. 177 #12a 4ln2x + ln(6/x) – 2ln2x

= ln(2x)4 + ln(6/x) – ln(2x)2

= ln16x4 + ln(6/x) – ln4x2

= ln(16x4∙6) x∙4x2

= ln(96x4) 4x3

= ln24x


Solving Log EquationsExample 1

log(x+1) = 1 – log(x-2)Restrictions: x>-1 and x>2

log(x+1) + log(x-2) = 1log((x+1)(x-2)) = 1

(addition law)

101 = (x+1)(x-2)(change to exponential form)



x2 – x – 2 = 10

x2 – x – 12 = 0(x+3)(x-4) = 0

(factoring)

x=-3 and x=4Because of the restrictions, we reject x=-3

S={4}



ln(x+2) = ln(-x+6) + ln(x-1)Restrictions: x>-2, x<6, x>1

ln(x+2) = ln((-x+6)(x-1))(x+2) = (-x+6)(x-1)

(divide both sides by ln)

x+2 = -x2 + 7x - 6(expand)

-x >-6 x<6



x2 – 6x + 8 = 0(x-2)(x-4) = 0

(factoring)

x=2 and x=4Both fit the restrictions

S={2,4}


Growth & DecayIntro to Exponential Functions


Formulas

GROWTH = (P)(1+interest rate)time

DECAY = (P)(1-interest rate)time


Example 3How much money will you have if you invest

700$ at 7.5% compounded annually for 15 years?

f(x) = (700)(1.075)15

= $2071.21


Example 4You buy a car for $25000. If it depreciates

by 4.3% annually, what’s the value of the car 10 years later?

f(x) = (25000)(1- 0.043)10

f(x) = (25000)(0.957)10

= $16108.66


Example 5An investment of $600 at 8% grows to

$7280. For how long was it invested?

7280 = (600)(1.08)x

12.13 =(1.08)x

log1.0812.13 = x(change to log form)

x = (log12.13)/(log1.08) = 32.43


Example 6An investment at 6% grows to $1296 in 12

years. What was the initial investment?

1296 = (P)(1.06)12

1296 =(P)(2.012)

$644.07 = P


Example 7An investment of $900 grows to $1340 in 8

years. What rate of interest did the investment earn?

1340 = (900)(1+r)8

1.48 =(1+r)8

(1.48)1/8 =(1+r)8∙(1/8)

(to get rid of the exponent)


Example 7An investment of $900 grows to $1340 in 8

years. What rate of interest did the investment earn?

1.051 = 1+r

0.051 = r

So 5.1%


HOMEWORK• TAKE HOME QUIZ

• Workbook p.137 #3,4,5,6 p.180-181 #27, 28

• Worksheet Side 2 #1,2

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