Identifying Horizontal Asymptotes

Both the numerator and denominator are linear (degree 1). Because the degrees are equal, there will be a horizontal asymptote at the ratio of the leading coefficients. In the numerator, the leading term is $t,$ with coefficient 1. In the denominator, the leading term is $10t,$ with coefficient 10. The horizontal asymptote will be at the ratio of these values:

This function will have a horizontal asymptote at $y=\frac{1}{10}.$

This tells us that as the values of t increase, the values of $C$ will approach $\frac{1}{10}.$ In context, this means that, as more time goes by, the concentration of sugar in the tank will approach one-tenth of a pound of sugar per gallon of water or $\frac{1}{10}$ pounds per gallon.