Question

Given the general definition of an exponential function

F(x) = Ca^x

Use the properties of exponents to show that

f(x+1)/f(x) = a

Answer 1

`f(x)=Ca^x\hspace{5em}f(x+1)=Ca^(x+1) \\\\[-0.35em] ~\dotfill\\\\ \cfrac{f(x+1)}{f(x)}\implies \cfrac{Ca^(x+1)}{Ca^x}\implies \cfrac{Ca^x\cdot a^1}{Ca^x}\implies \cfrac{Ca^x}{Ca^x}\cdot a^1\implies a^1\implies a`