Exponential Growth

Question

Over the past several months, a town’s rabbit population has been increasing at a rate of 82% per month. If the city’s current rabbit population is 6,528 , then what was the town’s rabbit population a month ago?

 

I am confused about how I would go about getting the population from the previous month. Would I use -1 to represent one month before the equation below?

 

R= 6,528*(1+(.82/12))^12*-1

Answer 1

Using a population growth equation: Where P is the original population number one month ago, the exponent represents the time between population increase. The problem states that the population increases monthly so that will be the units for t.

 

So if the population increases monthly, t will be 1, 2 months etc.. If the population were to increase yearly, nbsp;t would be 1, 2 years or partial year 1/12 = 1 month.

 

6,528 = P(1+0.82)¹

 

6,528 = 1.82P

 

6,528/1.82 = P

 

3,587 = P

 

 

Answer 2

Using the format given:

6528 = p(1.82)^t

Exponential growth and decay is usually

A = pe^rt