Final answer:
a) The equation to model the situation is P = 195,000(1 - 0.042)^t. b) The population of cheetahs after 15 months will be approximately 115,672.
Step-by-step explanation:
a) To write an equation to model the situation, we can use the formula for exponential decay: P = P0(1 - r)^t. In this case, the initial population (P0) is 195,000 and the rate of decline (r) is 4.2% per month (which is equivalent to 0.042). Therefore, the equation is P = 195,000(1 - 0.042)^t.
b) To find the population after 15 months, we can substitute t = 15 into the equation and solve for P. Plugging in the values, P = 195,000(1 - 0.042)^15 ≈ 115,671.6. Therefore, the population of cheetahs after 15 months will be approximately 115,672.