Exponentials and Logarithms Flashcards
(10 cards)
How can logₐb be interpreted?
logₐb can be interpreted as:
What is the power you need to raise a to to get b?
What does logₐa equal?
logₐa = 1
What does logₐ1 equal?
logₐ1 = 0
What is the natural log?
ln() which means log base e
Inverse functions of logs
aˡᵒᵍₐˣ = x logₐ(aˣ) = x
What are the three rules of logs?
logₐx + logₐy = logₐ(xy)
logₐx - logₐy = logₐ(x/y)
logₐxʸ = ylogₐx
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.
1000e^0.1t where t = 0
1000e^(0.1*0) = 1000e^0 = 1000
The initial population of shovel-snouted lizard is 1000.
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?
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.
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.
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.
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.
Why might this model not be appropriate for the long term?
After 77 years, when t = 77, the population of shovel-snouted lizard is predicted to be above 2 million. This number is too large to be realistic - the model hasn’t taken other factors such as predators into account.
