Flashcards in Exponentials and Logarithms Deck (10)

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1

## How can logₐb be interpreted?

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logₐb can be interpreted as:

What is the power you need to raise a to to get b?

2

## What does logₐa equal?

### logₐa = 1

3

## What does logₐ1 equal?

### logₐ1 = 0

4

## What is the natural log?

### ln() which means log base e

5

## Inverse functions of logs

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aˡᵒᵍₐˣ = x

logₐ(aˣ) = x

6

## What are the three rules of logs?

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logₐx + logₐy = logₐ(xy)

logₐx - logₐy = logₐ(x/y)

logₐxʸ = ylogₐx

7

##
The exponential growth of a population of shovel-snouted lizard can be modelled by the equation 1000e^0.1t where t is the time in years.

Work out the initial population.

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1000e^0.1t where t = 0

1000e^(0.1*0) = 1000e^0 = 1000

The initial population of shovel-snouted lizard is 1000.

8

##
The exponential growth of a population of shovel-snouted lizard can be modelled by the equation 1000e^0.1t where t is the time in years.

How many years will it be for the population to exceed 2000 shovel-snouted lizards?

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1000e^0.1t > 2000

e^0.1t > 2

ln(e^0.1t) > ln(2)

0.1t ln(e) > ln(2)

0.1t > ln(2)

t > ln(2) / 0.1

t > 6.9314718...

The population will have exceeded 2000 after 7 years.

9

##
The exponential growth of a population of shovel-snouted lizard can be modelled by the equation 1000e^0.1t where t is the time in years.

Predict the population of shovel-snouted lizard after 77 years.

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1000e^0.1t where t = 77

1000e^(0.1*77) = 1000e^7.7 = 2208347.992

Using the model the population of shovel-snouted lizard after 77 years is predicted to be 2208347.

10