The development of AstroWorld ("The Amusement Park of the Future") on the outskirts of a city will increase the city's population at the rate given below in people/year t yr after the start of construction. 5,700 t 11,000 The population before construction is 67,000. Determine the projected population 16 yr after construction of the park has begun. people

Complete question :

The development of AstroWorld ("The Amusement Park of the Future") on the outskirts of a city will increase the city's population at the rate given below in people/year t yr after the start of construction. 5,700√t + 11,000 The population before construction is 67,000. Determine the projected population 16 yr after the construction of the park has begun. people

486,200

Step-by-step explanation:

Given that the rate of change in population is represented by the function:

f(t) = 5,700√t + 11,000

To get the original function, we take the integral of the rate function because the rate of change is obtained by taking the derivate of the original equation

f(t) = 5,700t^1/2 + 11,000

Taking the integral of f with respect to t:

∫(5,700t^1/2 + 11,000)

[5700t^(1/2 + 1)] / (1/2 + 1) + 11000t + C

[(5700t^3/2)/ 3/2] + 11000t + C

Where C = constant

If population before construction = 67000

Then C = 67000

t = time = 16 years

Substitute values into the original change equation:

[(5700(16)^3/2)/ 3/2] + 11000t + 67000

[(5700 * 64) / 1.5] + 11000(16) + 67000

243200 + 176000 + 67000

= 486,200