Problem 4: Working for the wildlife department for the state of Colorado you are tasked with tracking the population of wild foxes. It is determined in 2015 that there were 71,500 foxes in Colorado and in this year's survey (2023) there are now 89,250 . Create an exponential model for the fox population and use it to predict the population in 2030 as well as predict when the population of foxes will reach 125,000 .
Answer
4. Predict when population reaches 125,000: \(125,000 = 71,500(1 + r)^{t-2015}\)
Step 1 ：1. Find growth factor: \(r = \left(\frac{89,250}{71,500}\right)^{\frac{1}{8-1}} - 1\)
Step 2 ：2. Exponential model: \(P(t) = 71,500(1 + r)^{t-2015}\)
Step 3 ：3. Predict fox population in 2030: \(P(2030) = 71,500(1 + r)^{2030-2015}\)
Step 4 ：4. Predict when population reaches 125,000: \(125,000 = 71,500(1 + r)^{t-2015}\)
