Answer
a) The population increased by $55.30-38.04=17.26 $ million people between 2030 and 2012, and by $80.38-55.30=25.08 $ million people between 2030 and 2048.
b) You can easily tell because there are 36 years between 2012 and 2048 which means that the population at 2048 is much higher than that of 2030 knowing that there are 18 years between both 2012 and 2030 and 2030 and 2048.
Work Step by Step
The problem describes an exponential function with the following parameters.
\begin{equation}
\begin{aligned}
a&= 38.04\\
r&= 2.1\%= 0.021\\
b&=1+r = 1.021
\end{aligned}
\end{equation}
A model of the population can be written as:
\begin{equation}
\begin{aligned}
P(t)&=a\cdot b^t\\
&=38.04\cdot (1.021)^t
\end{aligned}
\end{equation}
a) Set $t= 18$ for the number of years between 2030 and 2012 and $t= 36$ for the number of years between 2048 and 2012.
\begin{equation}
\begin{aligned}
P(18)&= 38.04\cdot (1.021)^{18}\\
&=55.30
\end{aligned}
\end{equation}\begin{equation}
\begin{aligned}
P(36)&= 38.04\cdot (1.021)^{36}\\
&=80.38
\end{aligned}
\end{equation}
The population increased by $55.30-38.04=17.26 $ million people between 2030 and 2012, and by $80.38-55.30=25.08 $ million people between 2030 and 2048.
b) You can easily tell because there are 36 years between 2012 and 2048 which means that the population at 2048 is much higher than that of 2030 knowing that there are 18 years between both 2012 and 2030 and 2030 and 2048.
