Define an exponential function, h(x), which passes through the points (1,16) and
(5, 1296). Enter your answer in the form axb^x
the equation is of the form
[tex]y=a(b)^x[/tex]we have
point (1,16)
so
For x=1, y=16
substitute
[tex]\begin{gathered} 16=a(b)^1 \\ 16=a\cdot b \end{gathered}[/tex]isolate the variable a
[tex]a=\frac{16}{b}[/tex]Point (5,1296)
For x=5, y=1,296
substitute
[tex]1,296=a(b)^5[/tex]substitute equation 1 in equation 2
[tex]1,296=(\frac{16}{b})\cdot b^5[/tex]solve for b
[tex]\begin{gathered} \frac{1296}{16}=b^4 \\ b^4=81 \\ b=3 \end{gathered}[/tex]Find the value of a
a=16/3
therefore
the equation is
[tex]y=\frac{16}{3}\cdot(3)^x[/tex]see the attached figure to better understand the problem
