Question

In 1981, the Australian humpback whale population was 350 and has increased at a rate of 14% each year since then.)

Write the equation for a function to that you could use to predict how many whales there would be in the year 2000: P(t) = _______
There would be about _______ humpback whales in the year 2018(round to the nearest whole number)

Answer 1

In 1981, the Australian humpback whale population was 350

Po = Initial population = 350

rate of increase = 14% annually

P(t) = Po*(1.14)^t

P(t) = 350*(1.14)^t

Where

t = number of years that have passed since 1981

Year 2000

2000 - 1981 = 19 years

P(19) = 350*(1.14)^19

P(19) = 350*12.055

P(19) = 4219.49

P(19) ≈ 4219

Year 2018

2018 - 1981 = 37 years

P(37) = 350*(1.14)^37

P(37) = 350*127.4909

P(37) = 44621.84

P(37) ≈ 44622

There would be about 44622 humpback whales in the year 2018