Finding exponential equations
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Transcript of Finding exponential equations
![Page 1: Finding exponential equations](https://reader036.fdocuments.in/reader036/viewer/2022070511/58a08cff1a28aba73f8b598b/html5/thumbnails/1.jpg)
Block 3
Finding Exponential Equations
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R
t
xxx
xx
x
xNot very straight!
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t
xxx
xx
x
x
Exponential
Equation?
R
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t
Rlog
log
xx
x
xx
xx
find equation with log R and log tin form log R = m log t + c
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t
Rlog
log
xx
x
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xx
need two points on linegradient
6
(4 , 34)m = 34 – 6
4 – 0 = 28/4
= 7
y = 7x + 6
log R = 7 log t + 6
do not want logs in equation
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log R = 7 log t + 6
logless!
want to change 6 → log10........
log statement log10 x = 6
translation x = 106
equation becomeslog R = 7 log t +
still some work to do!no need to always write 10
?
log10 106
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log R = 7 log t + log106
to get rid of logs want log…. = log….
Time for some log rules
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log R = 7 log t + log106
Neat Wee Rulelog R = log t7 + log106
Addition Rulelog R = log (t7 X 106)
R = 1000000t7
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TacticsGet straight line equation with logsChange everything to logsGet rid of the logs!!
Finding Exponential EquationsUsing Logs
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t
Rlog
log
xx
x
xx
xx
find equation with log R and log tin form log R = m log t + c
type y = axn
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t
Rlog
log
xx
x
xx
xx
need two points on lineFind Gradient
8
(13 , 34)m = 34 – 8
13 – 0 = 26/13
= 2
y = 2x + 8
log R = 2 log t + 8
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log R = 2 log t + 8
logless!
want to change 8 → log10?
log statement log10 x = 8
translation x = 108
equation becomeslog R = 2 log t + log 108
no need to always write 10
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log R = 2 log t + log108
Neat Wee Rulelog R = log t2 + log108
Addition Rulelog R = log (t2 X 108)
R = 100000000t2
to get rid of logs want log…. = log….
Eliminate LogsR = (t2 X 108)
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m = 2 , y int = 4→ y = 2x + 4→ log H = 2log M + 4
log H = 2log M + log104
log H = log M2 + log 10000log H = log 10000M2
H = 10000M2
log H
log M
4(4 , 12)
Key Question
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t
Rlog
xx
x
xx
xx
Equation log R = mt + c
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t
Rlog
xx
x
xx
xx
4
(6 , 7)m = 7 – 4
6 – 0 = 3/6
= 0.5
y = 0.5x + 4
log R = 0.5t + 4
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log R = 0.5t + 4
logless!
want to change 4 → log10
log statement log10 x = 4
translation x = 104
equation becomeslog R = log 100.5t + log 104
same for 0.5t
log10 x = 0.5t
x = 100.5t
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log R = log 100.5t + log 104
Addition Rule
log R = log (100.5t X 104)
R = 10000 X 100.5t
Eliminate LogsR = (100.5t X 104)
100.5 = 3.2R = 10000 X 3.2t
R = 10000 (3.2)t
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m = 0.25 , y int = 3→ y = 0.25x + 3→ log R = 0.25G + 3
Same tactics as previouslylog R = log 100.25G + log 103
Log Rulelog R = log (100.25G X 103)
Remove LogsR = (100.25G X 103) = (103 X 100.25G) = (103 X 1.78G)
R = 1000(1.78)G
log R
G
3(11 , 5)
Type y = abx
Both logless!
(100.25 = 1.78)
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m = 0.2 , y int = 1→ y = 0.2x + 1→ log F = 0.2P + 1
log F = log 100.2P + log 101
log F = log (100.2P X 10)F = (100.2P X 10) = (10 X 100.2P) = (10 X 1.58P)
R = 10(1.58)P
log F
P
1(8 , 3)
Type y = abx
Key Question
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If y = abt
Show that the relationship between log y and log b is linear
log y = log abt
reverse addition rulelog y = log a + log bt
Neat Wee Rule log y = log a + t log b
log y = t log b + log a
eh?log both sides
Annoying First Part of Question Sort of Thing
like y = mx + c → linear
i.e in the form y = mx + c