## Calculus: Early Transcendentals 8th Edition

(a) Trigonometric function plus a constant $$f(x)=a+b\cos x$$ (b) Linear descending function $$f(x)=-ax+b,\quad a,b>0$$
(a) The cosine function or some positive multiple of it oscillates around $x$ axis and has a maximum (one of them) when $x=0$. The data looks much like cosine function but shifted upwards which can be represented by adding a constant to a positive multiple of cosine: $$f(x)=a+b\cos x,\quad a,b>0.$$ (b) The points from the data look like they follow a line that decreases when $x$ increases so we will model with decreasing linear function of the form of $$f(x)=-ax+b, \quad a,b>0.$$ We have to take $b>0$ because the intercept with $y$ axis is positive.