Exponentials + logs Flashcards

1
Q

What happens with …..
1. an increase in b
2. negative b

A
  1. increases the steepness of the line (gradient)
  2. reflection in the x axis
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2
Q

What happens with …..
1. an increase in a
2. negative a

A
  1. an increase in y intrcept
  2. negative y intercept (a reflection in the x axis)
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3
Q

Relationship between a reciprocal base

A
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4
Q
A
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5
Q

what is the difference between exponetial growth curve and decay curve?

A
  • growth: population, disease
  • decay:
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6
Q
A
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7
Q
A
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8
Q
A

Asymptotes change

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9
Q
A
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10
Q
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11
Q
A
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12
Q

What are logarithms ?

A

The inverse of exponentials, gives the missing power

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13
Q

Convert log and exponential form

A
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14
Q

She thinks the logarithm graph

A
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15
Q
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16
Q
A
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17
Q

What is the Natural logarithm?

A
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18
Q
A
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19
Q

What is Euler’s number?

A

Where the gradient function = the function

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20
Q

What is the rule when differentiating exponential functions?

A
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21
Q
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22
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23
Q
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24
Q
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25
Q
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26
Q

What is the addition log law?

A
27
Q

What is the proof for the addition log law?

A
28
Q

What is the subtraction log law?

A
29
Q

What is the proof for the subtraction log law?

A
30
Q

What is the power law?

A
31
Q

What is the change of base law?

A
32
Q

What is the proof for the change in base law?

A
33
Q

What is the answer for these ?

A
34
Q

What is the simplified version for these logs expressions ?

A
35
Q

What is

A

logs are NOT distributive

36
Q
A

Use the log laws!

37
Q

What are the 3 different types of logs?

A
38
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39
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40
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41
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42
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43
Q
A
44
Q

What is linearisation and why is it done to exponentials?

A

Converting a function into straight line form: it becomes easier to collect information on them. This is done by Logs

45
Q

Linearise the equation

A
46
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47
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48
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49
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50
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51
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52
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53
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54
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55
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56
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57
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58
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59
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60
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61
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62
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63
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