[Video] Q7: 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 the population each year. which of the following functions best models the population p(t) of jackrabbits t years after 1788?

Explanation for Question 7 From the Math (No Calc) Section on the 2019 March Sat

Question seven says there were no jackrabbits in Australia before 1788, 2 when 24 jackrabbits were introduced by 1920, 3 the population of jackrabbits had reached 10 billion. 4 If the population had grown exponentially, 5 this was correspond to a 16.2% increase on average in 6 the population each year, which of the following functions, 7 best models, the population PFT of jackrabbits T years after 8 1780. So to figure out the answer to this problem, 9 we're going to need to create an equation in exponential form. 10 So I've got to have, I've written out the, the formula for an exponential 11 growth equation, which is what this problem is. 12 So EI represents the initial amount of whatever is increasing R 13 represents the rate of increase and T represents the time. 14 So we need to find what these values are in this problem, 15 and then plug those values in. So we know that the initial amount of 16 jackrabbits is 24, which means at the beginning of this equation should be 17 PFT is equal to 24. 18 And with that, we can eliminate a N D already. 19 Next we know that the increase is 16.2%. 20 So that means we need to add one to 0.162. 21 And so that should be 1.162. 22 And with that, we can eliminate the, 23 and we know that C is the correct answer.