Question

2. The following equation gives the number of blue whales on the planet, where t is the number of years since 2000. y = 2500 (0.72) a) How many whales are there in the year 2000? b) How many whales are there in the year 2005? c) What percent does the population increase/decrease each year? d) When will the population be 3000 whales? e) When will the population be 300 whales?

please show all the work and thank you! :)

Answer 1

Y = 2500 (0.72)^t y = 2500(0.72)^0 = 2500 for t = 0 2000 y = 2500 for 2005 t = 5 y = 2500(0.72)^5 = 423.729408 1 + r = 0.72 r = 0.28 It is decreasing Rate as 28% per year 3000 = 2500 (0.72)^t = 6/5 = 0.2 t n 0.72 = ln(1.x) t = ln(1.2)/ln(0.72) = -0.355 not possible 300 = 2500 (0.72)^t 3/25 = (0.72)^t t ln (0.72) = ln(0.12) t = ln(0.12)/ln(0.72) = 6.45429