Find the function

Question

The population density x miles from the center of a city is given by a function is given by

Q(x) = Ae^(-kx)

Find this function if it is known that the population density at the center of the city is 15,000 people per square mile and the density 10 miles from the center is 9,000 people per square mile

Answer 1

Q(0) = Ae^(0)

15000 = A ==>. Q(x) = (15000)e^(-kx)

Q(10) = (15000)e^(-k*10)

9000 = (15000)e^(-10k)

9/15 = e^(-10k)

3/5 = e^(-10k)

ln(3/5) = -10k

k = ln(3/5) / (-10)

k = ln(5/3) / (10) = 0.05108

Therefore: Q(x) = (15000)e^(-0.05108 x)