Rabbit population algebra help needed

Question

The rabbit population at the city park increases by 12% per year. If there are intially 183 rabbits in the city park. 

-Write a model for the population (y) in terms of years (t). Y=___

Find the rabbit population in 12 years. (Round to the nearest whole rabbit)  ____

[Estimate] When the rabbit population reaches 6509. It will happen between year____ and year ____

Answer 1

Function

y = 183(1+0.12)^t = 183(1.12)^t

Rabbit population in 12 years

y = 183(1.12)¹² ≈ 713

Time when rabbit population is 6509:

6509 = 183(1.12)^t

ln(6509/183) = t·ln(1.12)

ln(6509/183)/ln(1.12) = t

t ≈ 31.514

So, it will happen between year 31 and year 32.

Hope this helped!