Question

Define an exponential function, h(x), which passes through the points (1,16) and(5, 1296). Enter your answer in the form axb^xh(x) =

Answer 1

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

$y=a(b)^x$

we have

point (1,16)

so

For x=1, y=16

substitute

$\begin{gathered} 16=a(b)^1 \\ 16=a\cdot b \end{gathered}$

isolate the variable a

$a=\frac{16}{b}$

Point (5,1296)

For x=5, y=1,296

substitute

$1,296=a(b)^5$

substitute equation 1 in equation 2

$1,296=(\frac{16}{b})\cdot b^5$

solve for b

$\begin{gathered} \frac{1296}{16}=b^4 \\ b^4=81 \\ b=3 \end{gathered}$

Find the value of a

a=16/3

therefore

the equation is

$y=\frac{16}{3}\cdot(3)^x$

see the attached figure to better understand the problem