8.6 Natural logs Ln Pt 1 and 2 2015.notebook
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February 08, 2017
Solve for x:
5) Condense:
4) You purchased a new car for $24,900. It is depreciating at a rate of 10.3% per year. What will be the estimated value of the car in 4 year?
1) 2) 3)
WARM UP WITH CALCULATOR
8.6 Natural logs Ln Pt 1 and 2 2015.notebook
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HW 8.5 p. 465 Part II ANSWERS
p. 468
1. 2. Graphs3. 3 log s 5 log r4. 2 log6 3 + 2 log6 x + 2 log6 y5. log6 4 + 1/2 log6 x
8.6 Natural logs Ln Pt 1 and 2 2015.notebook
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February 08, 2017
8.6 Natural Logarithms
For the equation log 100 = x, what is the implied base?
If the base of a log is e, we use the ln button on the calculator so,loge is written ln
ln is said to be "the natural log"
All properties of logs apply to the natural log.
8.6 Natural logs Ln Pt 1 and 2 2015.notebook
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February 08, 2017
Write as a single ln.
PullPull
PullPull
8.6 Natural logs Ln Pt 1 and 2 2015.notebook
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PullPull
PullPull
Solve for x.
PullPull
8.6 Natural logs Ln Pt 1 and 2 2015.notebook
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PullPull
PullPull
PullPull
Solve for x. Get ex alone, then take ln of each side.
8.6 Natural logs Ln Pt 1 and 2 2015.notebook
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February 08, 2017
HOMEWORK 8.6 Part I
p. 472 #19 odd, 1537 odd, omit #29
8.6 Natural logs Ln Pt 1 and 2 2015.notebook
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February 08, 2017
8.6 Natural logs Ln Pt 1 and 2 2015.notebook
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PullPull
Warm Up Solve for x in each equation (#13).
1) 2)
3) 4) Evaluate:
8.6 Natural logs Ln Pt 1 and 2 2015.notebook
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February 08, 2017
55. x = 542.31 56. x = 1 58. x = 81.29
CHECK HW 8.6 Part 1 p. 472
8.6 Natural logs Ln Pt 1 and 2 2015.notebook
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February 08, 2017
Word Problems involving the Natural Log
What equation about growth do you know which involves e?
8.6 Natural logs Ln Pt 1 and 2 2015.notebook
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February 08, 2017
Solve the following problem. Remember to use A = Pert
An investment of $100 is now valued at $149.18. The interest rate is 8% compounded continuously. About how long has the money been invested?
PullPullWhat variable in the equation are you trying to find?
PullPullWill you need to use ln?
PullPullUse A=Pert
8.6 Natural logs Ln Pt 1 and 2 2015.notebook
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February 08, 2017
An initial investment of $200 is worth $315.24 after 7 years of continuous compounding. Find the interest rate.
PullPullWhat variable in the equation are you trying to find?
PullPullUse A=Pert
8.6 Natural logs Ln Pt 1 and 2 2015.notebook
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February 08, 2017
The population of Boringville is 800 dull folks. The number of residents is decreasing at a rate of 32% per year. How many years will it take before the number of inhabitants is 250 people?
8.6 Natural logs Ln Pt 1 and 2 2015.notebook
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February 08, 2017
HOMEWORK 8.6 Part2
P. 472 #28 even, 1438 even, 29, 4753 odd, 5659 all
8.6 Natural logs Ln Pt 1 and 2 2015.notebook
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EXTRA PROBLEMS
8.6 Natural logs Ln Pt 1 and 2 2015.notebook
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February 08, 2017
1) You have inherited land that was purchased for $20,000 in 1970. The value of the land increased by approximately 8% per year. What was the value of the land last year?
2) You purchased a new car for $24,900. It is depreciating at a rate of 10.3% per year. What will be the estimated value of the car in 4 year?
3) Solve for x:
4) Expand:
5) Condense:
6) Evaluate:
8.6 Natural logs Ln Pt 1 and 2 2015.notebook
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February 08, 2017
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