There are 225 wolves in a state park. The population is increasing at the rate of 15% per year. When will the population reach 500?

1 Answer
Apr 16, 2016

Answer:

Between years 5 and 6.

Explanation:

Population after #n# years is given by the formula
#color(white)("XXX")P_n=225xx(1.15)^n#

We are asked when
#color(white)("XXX")Pn = 500#

#color(white)("XXX")225xx(1.15)^n = 500#

#color(white)("XXX")rarr 1.15^n = 500/225=20/9#

#color(white)("XXX")log_(1.15) (20/9) = n#

Using a calculator
#color(white)("XXX")log_1.15 (20/9) ~~5.7133#