Question

The size of a certain population of wild horses varies because of certain ecological pressures. The population can be modelled using the formula, P(x)= 20cos60x+80, where P(x) is the population of horses, while x is the number of years since 2009. a) How many horses were there in 2010? b) How many horses should there be in 2025?

Answer 1

a. 90

b. 70

Explanation:

What we need to do here is make substitutions for x.

We proceed as follows;

P(x) = 20cos60x + 80

x is the number of horses since 2009, so for 2010, x = 2010-2009 = 1

Substitute this;

P(x) = 20Cos60(1) + 80 = 20Cos60 + 80 = 10 + 80 = 90

Kindly recall that cos 60 = 0.5

For 2025, x = 2025 - 2009 = 16

Substitute this value;

P(x) = 20cos60(16) + 80

P(x) = 20cos960 + 80

Recall, cos960 = -0.5

P(x) = 20(-0.5) + 80

P(x) = -10 + 80

P(x) = 70