Question

Write en exponential function y=ab^x for a graph that includes the given points. (2,135) and (4,1215)

Answer 1

`y=ab^x \\ b>0 \\ \\ (2,135) \\ x=2 \\ y=135 \\ \downarrow \\ 135=ab^2 \\ a=(135)/(b^2) \\ \\ (4,1215) \\ x=4 \\ y=1215 \\ \downarrow \\ 1215=ab^4 \\ a=(1215)/(b^4)`


`(135)/(b^2)=(1215)/(b^4) \\ 135b^4=1215b^2 \ \ \ |/ 135b^2, \ b>0 \\ b^2=9 \\ b=-3 \ \lor \ b=3 \\ b>0 \\ b=3 \\ \\ a=(135)/(b^2)=(135)/(3^2)=(135)/(9)=15 \\ \\ \boxed{y=15 * 3^x}`