The population of wild horses on a wildlife refuge decreased from 110 to 99 in a year. If this trend were to continue, what exponential equation could be used to predict the horse population in the future?
a) y = 110(1.1)^x
b) y = 99(0.9)^x
c) y = 99(1.1)^x
d) y = 110(0.9)^x
The population of wild horses decreased from 110 to 99, which means it decreased by 11 horses. We can use this information to determine the rate of decrease, which is 11/110 or 0.1.
Since the population is decreasing, we need to use a decay function, which is of the form y = a(1 - r)^x, where a is the initial population, r is the rate of decrease, and x is the number of years.
Substituting the given values, we get:
y = 110(1 - 0.1)^x
Simplifying, we get:
y = 110(0.9)^x
Therefore, the answer is (d) y = 110(0.9)^x.