Answer
$0.37$
In the long run, if this trend continues, the annual spending on police will be $ 37\%$ of the total spending on law enforcement.
Work Step by Step
$f(t)=\displaystyle \frac{P(t)}{P(t)+C(t)+J(t)}=\frac{1.745t+29.84}{(1.745+1.097+1.919)t+(29.8+10.65+12.36)}$
$=\displaystyle \frac{1.745t+29.84}{4.761t+52.85}$
Using theorem 10.2, since both are polynomials, we can calculate the limit of $f(t)$ as $ t\rightarrow\pm\infty$ by ignoring all powers of $t$ except the highest power in both the numerator and denominator.
$\displaystyle \lim_{t\rightarrow\infty}f(t)=\lim_{t\rightarrow\infty}\frac{1.745t}{4.761t}=\lim_{t\rightarrow\infty}\frac{1.745}{4.761}\approx 0.37$
In the long run, if this trend continues, the annual spending on police will be $ 37\%$ of the total spending on law enforcement.
