Question

If Farmer Jane tells you the number of rabbits on her farm starts at 100 (in year 0) and triples every year, complete the table below to show her how many rabbits she will have in 3 years.

What should the base be when something triples? ________
How do you know? Explain in words using your knowledge of exponents.

Answer 1

An exponential function is written

y = abx

So we need to find a and b.

Notice that at the start of the problem, we are zero months in. In that case, x=0. Substitute zero into the exponential function, recall that (almost anything)0 equals 1 and notice that

y = ab0

y = a(1)

y = a.

Next, recall that at the start of the problem, y=10. So we have found a = 10.

Now, if the population doubles every month, what do you expect to get when x=1? Take your answer to that, along with x=1 and solve for the base b.