Maths-
General
Easy
Question
There were no jackrabbits in Australia before 1788 when 24 jackrabbits were introduced. By 1920, the population of jackrabbits had reached 10 billion. If the population had grown exponentially, this would correspond to a 16.2% increase, on average, in population each year. Which of the following functions best models the population p(t) of jackrabbits t years after 1788?
- p (t) = 1.162 (24)t
- p (t) = 24 (2)1.162t
- p (t) = 24 (1.162)t
- p (t) = (24 * 1.162)t
Hint:
Exponential growth means when there is an increase in initial number by the same percentage/ factor over equal time intervals. This can be represented in mathematical form as follows-
f (x) = a 
where-
a = Initial number
r = rate of increase
t = time during which the increase occurred
The correct answer is: p (t) = 24 (1.162)t
Step-by-step solution:-
Since in the given question, the number of jackrabbits increases by a constant rate of 16.2% every year for t years, it is an example of exponential growth.
∴ applying the above function where-
f (x) = function modelling the population of jackrabbits = p (t)
a = Initial number of jackrabbits = 24
r = rate of increase every year = 16.2%
t = time during which the number of rabbits increased,
f (x) = a
∴ p (t) = 24 
∴ p (t) = 24 (1 + 0.162)t
∴ p (t) = 24 (1.162)t
Hence, option(c) is the correct option.
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