Question

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

Answer 1

$y=ab^x \\ b>0 \\ \\ (2,135) \\ x=2 \\ y=135 \\ \downarrow \\ 135=ab^2 \\ a=\frac{135}{b^2} \\ \\ (4,1215) \\ x=4 \\ y=1215 \\ \downarrow \\ 1215=ab^4 \\ a=\frac{1215}{b^4}$

$\frac{135}{b^2}=\frac{1215}{b^4} \\ 135b^4=1215b^2 \ \ \ |\div 135b^2, \ b>0 \\ b^2=9 \\ b=-3 \ \lor \ b=3 \\ b>0 \\ b=3 \\ \\ a=\frac{135}{b^2}=\frac{135}{3^2}=\frac{135}{9}=15 \\ \\ \boxed{y=15 \times 3^x}$