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?
To determine the exponential equation that could be used to predict the horse population in the future, we need to find the growth rate (r).
First, we calculate the difference in population from one year to the next: 99 - 110 = -11.
Next, we divide the difference by the initial population: -11 / 110 = -0.1.
The growth rate (r) is the decimal form of the percentage change, so the growth rate in this case is -0.1.
Finally, we can use the formula for exponential growth: P(t) = P₀ * e^(rt), where P(t) is the future population, P₀ is the initial population, e is Euler's number (approximately 2.71828), r is the growth rate, and t is time.
Therefore, the exponential equation to predict the future horse population is P(t) = 110 * e^(-0.1t), where t is measured in years.