Question

suppose a rabbit population of 10 rabbits trippled every 2 months. write an exponential function that represents the population of rabbits and define the variable x. How many rabbits will exist after two years

Answer 1

exponential function that represents the population of rabbits :
`10*3^{(x)/(2) }`

number of rabbits after 2 years :
`10*3^(12)`

Explanation:

• initially there are 10 rabbits. since the will be trippled every 2 months, i have multiplied it with
  `3^{(x)/(2) }`. I have divided x by 2 because, here x represents number of months and it will be trippled only AFTER EVERY 2 MONTHS.

• variable x: it represents number of months.

• two years= 2*12 months

• now substitute x= 2*12 in the above function.

• number of rabbits after 2 years =
  `10*3^{(2*12)/(2) }  = 10*3^(12)`