Suppose that you are monitoring island endemic cricket population that has recently become threatened due to an invasive parasitoid wasp species that is attacking its members. From observations of birth and death rates, you estimate that the intrinsic growth rate of the cricket population to be ,which has a 95% confidence interval of:

95% C.I. for r = [-0.01, -0.1]

Since the entire confidence interval for your estimate of r is negative, your data imply that the population will decline over time.

Question 2.The current size of the cricket population is 5,000 individuals. Assume that the current conditions of parasitism do not change and, thus, r remains constant over time. Use your point estimate for r () and the model presented above to predict the amount of time it will take for the population size to decline below 50 individuals, which is the threshold for a "critically endangered" classification. Show how you arrived at your conclusion. [1 point]

Scoring:Full credit for providing the correct answer andshowing how the answer was obtained (i.e., submit the R code and relevant simulation output to justify the answer OR present a detailed mathematical solution to the question).