Answer
a) $P=106 e^{0.018 t}$
b) In 2018, the formula predicts that world poultry production will be about 116 million tons.
c) The production will be 120 million tons late in the year 2019.
Work Step by Step
a) We are given that $P=106$ when $t=0$, we have $a=106$. Since $k=0.018$,the poultry population is
$$
P=106 e^{0.018 t}
$$ b) When $t=5$, we have $P=106 e^{0.018(5)}=115.98$. In 2018, the formula predicts that world poultry production will be about 116 million tons.
c) Graph the functions $P=106 e^{0.018 t}$ and $P=120$ . We see that when $P=120$ we have $t=6.9$. The production will be 120 million tons late in the year 2019.
