Download Warmup Write the following numbers as decimals and percents

Warmup
Write the following numbers as decimals and percents
1.
2.
3.
1
Standard 6.3
Writing Exponential Equations
Standard 6.3 Developing: Given and equation, identify the
growth/decay factor, the growth/decay rate and the initial value.
Proficient: Write exponential growth and decay models from
context and make predictions.
2
Identify if the equation shows growth or decay then identify the growth/decay factor and the initial value.
1a.
1b.
1c.
growth/decay:
factor:
initial value:
3
Percent means "per hundred", or, the fraction over 100
Examples:
2a.
1 =
2b.
2 =
2c.
0.6 =
To compare numbers using percents,
divide the second number by the first number, then multiply by 100%
Examples:
2d. 1st Value: 1 2nd value: 2
2e. 1st Value: 3.0 2nd value: 3.6
2f. 1st Value: 2.4 2nd value: 1.8
4
5
Percent Increase is
the amount more than 100% of one number compared to another.
How to calculate: Divide the 2nd number by the 1st, then multiply by 100%, then subtract 100%.
Examples:
st 2g. 1 Value: 1 2nd value: 2
2h. 1st Value: 3.0 2nd value: 3.6
2i.
1st Value: 0.8 2nd value: 4.0
6
Percent Decrease is
the amount less than 100% of one number compared to another.
How to calculate: Divide the 2nd number by the 1st, then multiply by 100%, then subtract from 100%.
Examples:
st 2g. 1 Value: 2 2nd value: 1
2h. 1st Value: 4.0 2nd value: 3.6
2i.
1st Value: 8.0 2nd value: 0.8
What if the two numbers are the same?
7
Exponential Growth Rate
In exponential functions the growth factor is the ratio of outputs.
For example:
Growth factor:
Ratio of Outputs:
Percent Increase:
Decimal Increase:
8
Exponential Growth Rate
The exponential growth rate ( r ) is the decimal or percent increase of the output values. To calculate r in percent: Find the growth factor, multiply by 100%, then subtract 100%
To calculate r as a decimal: Find the growth factor then subtract 1
To relate to growth factor ( b ): Percent:
Decimal:
Examples: Growth factor b, growth rate r (% and decimal)
3a.
3b.
3c.
For an exponential equation to show growth, what is true about the growth factor?
9
Exponential Decay Rate
In exponential functions the decay factor is the ratio of outputs.
The exponential decay rate ( r ) is the decimal or percent decrease of the output values. To calculate r in percent: Find the decay factor, multiply by 100%, then subtract from 100%
To calculate r as a decimal: Find the decay factor then subtract from 1
To relate to decay factor ( b ): Percent:
Decimal:
Examples: Decay factor b, decay rate r (% and decimal)
3a.
3b.
3c.
For an exponential equation to show decay, what is true about the decay factor?
10
Summary
For a : Initial value
If b > 1 : Growth
then b: Growth factor
and r: Growth rate b = 1 + r
If b < 1 : Decay
then b: Decay factor
and r: Decay rate b = 1 ­ r
11
12
13
Classwork
Homework
H63B
14
15