## Calculus: Early Transcendentals 8th Edition

(a) We model with $$f(x)=a b^x, \quad a>0,\quad b>1.$$ (b) We model with $$f(x)=\frac{a}{x},\quad a>0.$$
(a) The points from the data look like some exponential growth. The exponential function will grow if the basis is greater than one and if the multiplying constant is positive so we have $$f(x)=a b^x,\quad a>0,\quad b>1.$$ (b) These points look like they follow a hyperbola that has both $x$ and $y$ axes as asymptotes. The general equation for such hyperbola is given by $$f(x)=\frac{a}{x},\quad a>0,$$ and we will take it as the model for the given data.