Answer
a) $P=6.92(0.9917)^t$
b) The predicted population of Bulgaria in 2030 is about $6.06$ million people.
c) The year $2079$
Work Step by Step
(a) We know that the growth factor is $1-0.0083=0.9917$ and the initial population is 6.92.The required exponential function is
$$
P=6.92(0.9917)^t
$$ b) $2030$ corresponds to $t=2030-2014=16$, so we have $P=6.92(0.9917)^{16}=6.06$. The predicted population of Bulgaria in 2030 is about $6.06$ million people.
c) We have:
Percent change $=\frac{6.06-6.92}{6.92}=-0.124=-12.42 \%$. The percent drop over this period is expected about $12.42 \%$.
d) See the figure. We see that $t=65.8$ when $P=4$. The population is expected to be 4 million in approximately the year $2014+65.8=2079.8$, that is, 2079 .
