Hello wannabeleader!
In order to find the answer, we must take the derivative of the
function you provide with respect to t. Recall that the derivative
shows by how much the function is changing when the variable you're
deriving with respect to (t, in this case) increases one unit (in this
case, one unit is one year).
We have that:
P = 1.15*(1.014)^t
The derivative of this function is:
dP/dt = 1.15*ln(1.014)*(1.014)^t =
(If you don't know how to calculate a derivative, the following link might help)
Mathwords: Derivative Rules
http://www.mathwords.com/d/derivative_rules.htm
Now we just need to plug the appropiate values of t in the derivative
to get the answer. At the start of 1993, we are zero years from the
start of 1993; thus t=0. Plugging t=0, we get:
dP/dt = 1.15*ln(1.014)*(1.014)^0 = 0.0159883...
Since this value is in billions, we get that the population grows at
15.98 million people per year at the start of 1993.
At the beginning of 1995, t=2. So
dP/dt = 1.15*ln(1.014)*(1.014)^2 = 0.01643914...
Again, this means that the population grows at 16.43 million people
per year at the start of 1995.
I hope this helps!
Best wishes,
elmarto |