Find a Formula for an exponential function satisfying $f(1)=5$ and $f(3)=d$.

Question

Can anyone help me find a formula for an exponential function satisfying $f(1)=5$ and $f(3)=d$ with the answer in terms of the parameter $d$.Is anyone able to help me out with this question? I don't really know where to begin and how to find the answer.

Answer 1

Let $f(x):=a\cdot b^x$. Then $$5=a\cdot b\qquad d=a\cdot b^3=5\cdot b^2\implies b=\sqrt{\frac{d}5}\implies a=\frac5b=\frac{5\sqrt5}{\sqrt d}$$ Therefore

$$f(x)=\frac{5\sqrt5}{\sqrt d}\cdot \bigg(\sqrt{\frac{d}5}\bigg)^x$$