SOLUTION: The population of a colony of rabbits grows exponentially. The colony started with 10 rabbits and five years later, there were 340 rabbits. 1) Write a formula for the populatio

Algebra ->  Exponential-and-logarithmic-functions -> SOLUTION: The population of a colony of rabbits grows exponentially. The colony started with 10 rabbits and five years later, there were 340 rabbits. 1) Write a formula for the populatio      Log On


   

Question 751815: The population of a colony of rabbits grows exponentially. The colony started with 10 rabbits and five years later, there were 340 rabbits.
1) Write a formula for the population of the colony of rabbits as a function of the number of years since it was founded (but not "e" base).
2) How many rabbits will there be TEN years after the start of the colony?
3) Approximately how long will it take for the population of the colony to reach 1000 rabbits?


Thank you in advance for your time and assistance.
Answer by josgarithmetic(39620) About Me  (Show Source):
You can put this solution on YOUR website!
Look at each year symbolically step by step.
Let r = the growth rate in a year in fractional form, or decimal form.
1 year-------- 10%2A%281%2Br%29
2 year -------- 10%2A%281%2Br%29%5E2
3 year --------10%2A%281%2Br%29%5E3
4 year ------- 10%2A%281%2Br%29%5E4
5 year -------highlight%2810%2A%281%2Br%29%5E5=340%29

The function will be p%28x%29=10%281%2Br%29%5Ex where x is the number of years. You would use the highlighted '340' equation to find the growth rate, r and then use this in p(x) accordingly.