An animal reserve in Arizona had 150 wild antelope. Due to drought, the number of wild antelope decreased at the rate of $7 \%$ per month. How many months will it take for the number of wild antelope to be one-half of their original number? $\frac{\log (0.5)}{\log (0.07)}$ months $\frac{\log (75)}{\log (0.07)}$ months $\frac{\log (0.5)}{\log (0.93)}$ months $\frac{\log (150)}{\log (0.93)}$ months $\frac{\log (75)}{\log (150)}$ months

Step 1 ：The problem is asking for the time it will take for the number of antelope to decrease to half of their original number. This is a problem of exponential decay, where the number of antelope decreases by a certain percentage each month.

Step 2 ：The general formula for exponential decay is \(N = N0 * (1 - r)^t\), where \(N\) is the final amount, \(N0\) is the initial amount, \(r\) is the rate of decay, and \(t\) is time.

Step 3 ：We want to find \(t\), so we can rearrange the formula to \(t = \log(N/N0) / \log(1 - r)\).

Step 4 ：The initial number of antelope is 150, the final number is half of that (75), and the rate of decay is 7% or 0.07. So we can substitute these values into the formula to find the time it will take for the number of antelope to decrease to half.

Step 5 ：\(N0 = 150\)

Step 6 ：\(N = 75.0\)

Step 7 ：\(r = 0.07\)

Step 8 ：\(t = \log(75/150) / \log(1 - 0.07)\)

Step 9 ：The result is approximately 9.55 months. However, since the number of months must be an integer, we should round this up to the nearest whole number, which is 10 months.

Step 10 ：Final Answer: The number of months it will take for the number of wild antelope to be one-half of their original number is approximately \(\boxed{10}\).