Final answer:
The yearly bear population growth function P = 120(1.016)^t can be rewritten for the weekly growth rate by adjusting the exponent to t/52. The weekly growth rate, calculated as 1.016^(1/52) - 1, is approximately 0.0307% per week.
Step-by-step explanation:
The given function representing the total bear population is P = 120(1.016)^t, where P is the population, 1.016 is the annual growth rate, and t is the time in years. To convert this to a weekly growth rate, we need to account for the number of weeks in a year. Since there are approximately 52 weeks in a year, we would raise 1.016 to the power of 1/52.
Therefore, the function rewritten to reflect the weekly growth rate is P = 120(1.016)^(t/52). To calculate the numeric value of the weekly growth rate, we calculate 1.016^(1/52) - 1, which gives us an approximation of 0.000307 or 0.0307% growth per week.