Question

Write an exponential function y=ab^x whose graph passes through the given points (1,2), (3,32)

Answer 1

`\begin{gathered} P1(1,2) \\ f(1) \\ 2=ab^{}\text{ (1)} \\ P2(3,32) \\ f(2) \\ 32=ab^3(2) \\ from\text{ (1)} \\ a=(2)/(b) \\ \text{now in 2 } \\ 32=((2)/(b))\cdot b^3 \\ 32=2b^2 \\ (32)/(2)=b^2 \\ 16=b^2 \\ b=\sqrt[]{16} \\ b=4 \\ f(x)=a\cdot4^x \\ U\sin g\text{ point 2 (3,32)} \\ 32=a\cdot4^3 \\ 32=64a \\ a=(32)/(64) \\ \\ a=(1)/(2) \\ \\ f(x)=(1)/(2)\cdot4^x \\ \text{The exponential function is }f(x)=(1)/(2)\cdot4^x \end{gathered}`