Question

The population of fish in a pond can be modeled with the sinusoidal function p=6000sin(π10t)+47000, where t is the number of years after 2009. To the nearest whole number, what was the population in the year 2015?

Answer 1

The population of fish in the year 2015 is approximately 50280 fish.

Step-by-step explanation:

The population of fish in the year 2015 can be determined by substituting t = 2015 - 2009 = 6 into the given sinusoidal function p = 6000sin(π/10t) + 47000. So, p = 6000sin(π/10*6) + 47000 = 6000sin(3π/5) + 47000.

To evaluate sin(3π/5), we first need to know the value of π. The approximate value of π to 2 decimal places is 3.14. Therefore, sin(3π/5) = sin(3 * 3.14/5) = sin(9.42/5).

Using a calculator, we find that sin(9.42/5) ≈ 0.58. So, the population of fish in the year 2015 is approximately 6000 * 0.58 + 47000 ≈ 50280 fish.