1.

The population of deer on an island is given by p(x)=100(0.85)^x, where c represents the number of years. determine the percent of change for the population of deer per year.

Answer»

Given : The population of deer on an island is given by p(X)=100(0.85)^x

To find :  the PERCENT of CHANGE for the population of deer per year.

Solution:

population of deer on an island is given by p(x)=100(0.85)^x

Population after n year = 100(0.85)ⁿ

Population after n+1 year = 100(0.85)ⁿ⁺¹

Change in population = 100(0.85)ⁿ⁺¹ - 100(0.85)ⁿ

= 100(0.85)ⁿ( 0.85 - 1)

= 100(0.85)ⁿ(-0.15)

= 15(0.85)ⁿ

% change in population  =   100  x  (-15(0.85)ⁿ) /  100(0.85)ⁿ

= -15 %

-ve sign shows decrease

Hence  15 % decrease in population every year

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