Question

Find an exponential function having the given values. Explain, please.

f(0)=64, f(2)=4

Answer 1

\[f(x)=C\cdot a^x\quad,\quad a>0\quad\wedge\quad a\neq 1\]\[f(0)=C\cdot a^0=C=64\]\[f(2)=C\cdot a^2=4\quad,\quad a=\sqrt{4/C}=\sqrt{4/64}=1/4\]\[f(x)=64\cdot\frac{1}{4^x}=4^3\cdot\frac{1}{4^x}=4^{3-x}=2^{2(3-x)}\]