Unit 10 Day 2 Growth and Decay welcome 1. Take out notebook, pencil and calculator 2. Take out assignment from yesterday 3. Complete the Warm Up: You arrived home at 3:00 PM to find that your room is too cold so you try to adjust the thermostat. The current temperature of the room is 60 degrees Fahrenheit. In an attempt to get warmer, you increase the temperature by 5% every hour. An hour later, it is still not warm enough. So you continue this process until the temperature is a balmy 72 degrees. At what time are you finally comfortable? Warm up: Write a recursive formula and fill in table. R.F. Figure 1 2 3 7 9 Perimeter 4 8 12 16 n 1 2 3 4 9 u n 2.3 3.5 4.7 9.5 R.F.
Transcript
Unit 10 Day 2 Growth and Decay
welcome1. Take out notebook, pencil and calculator
2. Take out assignment from yesterday
3. Complete the Warm Up:
You arrived home at 3:00 PM to find that your room is too cold so you try to adjust the thermostat. The current temperature of the room is 60 degrees Fahrenheit. In an attempt to get warmer, you increase the temperature by 5% every hour. An hour later, it is still not warm enough. So you continue this process until the temperature is a balmy 72 degrees. At what time are you finally comfortable?
Warm up: Write a recursive formula and fill in table.
R.F.
Figure 1 2 3 7 9
Perimeter 4 8 12 16
n 1 2 3 4 9
un 2.3 3.5 4.7 9.5
R.F.
Unit 10 Day 2 Growth and Decay
agenda 05 MIN Warm Up
05 MIN Homework ?'s
20 MIN Lesson 10.2 Notes
15 MIN Assignment OYO
homework answers
Unit 10 Day 2 Growth and Decay
homework answers
homework answers
Unit 10 Day 2 Growth and Decay
homework answers
unıt 10: sequences
Modeling Growth & Decay
I can define orally and in writing: recursive formula, recursive rule, common difference, geometric sequence, common ratio
I can a recursive formula to real world situations like loans and investments.
I can read and write recursive formulas with subscript notation.
I can find terms of a sequence given recursively.
Learning Targets
Unit 10 Day 2 Growth and Decay
*You will need a graphing calculator today!Given the common ratios below, decide whether they show growth or decay. Then state the percent gain/loss.
1) 1.05
2) .84
3) 1.35
4) .93
5) 1
Growth and Decay
Growth:
Decay:
For Growth r > ____
For Decay r < ___ (but > 0)
Unit 10 Day 2 Growth and Decay
Identify if the recursive routine represents growth or decay and state the percent change.
a) Un = (1 + 0.25)Un1
b) Un = (1 0.3)Un1
c) Un = (1.54)Un1
d) Un = (.43)Un1
growth or decay
common ratio percent change
growth or decay
common ratiopercent change
growth or decay
common ratiopercent change
growth or decay
common ratio percent change
U1 = 15 Un = Un-1 + 5 where n > 2You MUST count.
15 enter
ans + 5 enter, enter...
1,15 then press enter.
Next, enter this:
Ans (1)+1, Ans (2) +5
Calc. counts.
Can you explain how?
Unit 10 Day 2 Growth and Decay
a) Identify the sequence as growth or decay.
b) Find the common ratio.
c) Give the percent change.
d) Write the recursive formula.
e) Find U20
14, 23.52, 39.5136, 66.382848, ...Ex 1)
a) Identify the sequence as growth or decay.
b) Find the common ratio.
c) Give the percent change.
d) Write the recursive formula.
Ex 2) 59, 27.73, 13.0331, 6.125557, ...
Unit 10 Day 2 Growth and Decay
c) What is the percent change?
U1 = 14 Un = Un1 0.3, where n > 2
Given the following example:
a) List the first four terms in the sequence
b) What is the common ratio?
d) Plot this situation on a graph.
STAT Edit 2nd y =
WINDOW GRAPH
Unit 10 Day 2 Growth and Decay
Suppose Mr. Scardigli's Ford Focus cost $18,455.00 and loses one fifth of its value every year. a) Write a recursive formula for this situation.
b) Find its value when it is 6 years old.
c) When will its value fall less than $2000?
Suppose the recursive formula U2004 = 5000 Un = (1+.05)Un1, where n > 2005
describes an investment made in the year 2004.
Give realworld meanings for the numbers 5000 and 0.05.
Unit 10 Day 2 Growth and Decay
OYO: U1 = 12
Un = Un1 1.25, where n > 2
a) List the first four terms in the sequence
b) What is the common ratio?
c) What is the percent change?
I can define orally and in writing: recursive formula, recursive rule, common difference, geometric sequence, common ratio
I can a recursive formula to real world situations like loans and investments.
I can read and write recursive formulas with subscript notation.
I can find terms of a sequence given recursively.
Did you meet the goal?
Assignment:1.2 pg. 41 44
1 4, 610, 15, 16, 1820
Quiz #
1??
Unit 10 Day 2 Growth and Decay
Unit 10 Day 2 Growth and Decay
Unit 10 Day 2 Growth and Decay
1.51.03 0.92
0.4
a. growth 50% increase b. decay 60% decrease
c. growth 3% increase d. decay 9% decreaseu1 = 80
un = 1.03u n-1
u1 = 100
un = 1.5u n-1
u1 = 208
un = 0.92u n-1
u1 = 73.4375
un = 0.4u n-1
ii decay
i growth
iii constant
0.811 inches
21 bounces, 31 bounces
100 starting height, 0.2 is the percent loss
$250,000 starting amount, 2.5% annual interest
a. b. about 29 or 30 employees
year 1: 2 12 + 2 + 3 + 3 + 4 + 5 = 29
year 2: 3
year 3: 3 (or 4)
year 4: 4
year 5: 5
Unit 10 Day 2 Growth and Decay
u0 = 2000 un = 1.085u n-1 8.5%
14 years ($6266.81)
3; I did 162/18 = 9 3 2 = 92, 6, ... 54, ... 486, ... 1458, ... 13122
118,098
248.6 million I solved the equation (1 + 0.132)x = 281.4
