Question

A population grows from an initial size of 10 people to an amount P(t), given by P(t)=10(3+0.5t+t^3) where t is measured in years from 1996. Find the acceleration in the population t years from 1996.
a)60t people per year^2
b)30t people per year^2
c)600t people per year
d)36t people per year^2

Answer 1

Since the required is the acceleration in the population, the second derivative of the equation is needed.
The first derivative has to be determined first.
dP(t)/dt = 10(0.5+3t^2)
Next, the second derivative can be determined using the first derivative:
d2P(t) = 10(6t) = 60t
Since it's acceleration, the unit is per year^2

THE ANSWER IS a) 60t people per year^2