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)^×
B. y=99(0.9)×
C. y=99(1.1)^×
D. y=110(0.9)^×
The population of wild horses on the wildlife refuge decreased from 110 to 99 in a year. Since the population is decreasing, we can use the equation y = a(1 - r)^x, where y is the population after x years, a is the initial population, and r is the rate of decrease.
In this case, the initial population is 110 and the population decreased by 9, so the rate of decrease is 9/110 = 0.0818.
Therefore, the exponential equation that could be used to predict the horse population in the future is:
y = 110(1 - 0.0818)^x
Simplifying this equation, we get:
y = 110(0.9182)^x
So the correct answer is D. y = 110(0.9)^x.