Q. 41. Find all asymptotes of the curve \( x^{3}+y^{3}=3 a x y \). (Bhopal 1991, 2000; Sagar

(a) Find an exponential function of the form \( f(t)=y_{0} b^{t} \) to model these data in which \( t=0 \) corresponds to 2004 . \( f(t)=31.22 \cdot(1.072)^{t} \) (Use integers or decimals for any numbers in the expression. Round to the nearest thousandth as needed.) (b) If the model remains accurate, what was the predicted rent per square foot in 2016 ? If the model remains accurate, the predicted rent per square foot in 2016 was \( \$ \square \). (Round to the nearest hundredth as needed.)

16 Find the horizontal asymptote, if any, of the graph of the rational function. \( h(x)=\frac{4 x^{3}}{2 x^{2}+1} \)

Find the vertical asymptotes, if any, of the graph of the rational function. \( f(x)=\frac{x}{x^{2}+8} \)

\( 1 \leftarrow \quad \) Find the vertical asymptotes, if any, of the graph of the rational function. \[ g(x)=\frac{x}{x^{2}-1} \]

The annual amount of crude-oil production in a country (in millions of barrels) can be approximated by the function \( f(t)=1725(1.044)^{\mathrm{t}} \), where \( t=8 \) corresponds to the year 2008. (a) Find the amount of production in 2014 . (b) If the trend continues, find the amount of production in 2025 . (a) The amount of production in 2014 was \( \square \) million barrels. (Round to the nearest whole number as needed.)