# Math Help - Population problem

1. ## Population problem

The population P, of China in billions can be approximated by
P=1.15(1.055)^t where t is the number fo years since the start of 1993.

a.According to this model what was the average rate of change of the population from the start of 1996 until the start of 2000?
b.According to this model how fast was the population growing at the start of 1996.

2. For the first problem, we may use our average value formula

$\frac{1}{b-a}\int_a^b P'(t)\,dt=\frac{1}{4}\int_3^7 (1.15)\cdot(1.055)^t\cdot \ln 1.055\,dt.$

Here, we have used the rule

$\frac{d}{dx}(a^x)=a^x \ln a.$

Solving the second problem amounts to finding $P'(t)$ at $t=3$.