Question

write an exponential function y=ab^x for a graph that includes (2,4) and (3,16)

Answer 1

Answer:

$y = \frac{1}{4} (4) {}^{x}$

Step-by-step explanation:

An exponetial function is represented by

$y = ab {}^{x}$

where a is the vertical stretch or initial rate and b is the factor or base.

Since neither point have a x coordinate of zero. Use this method.

plug in y value into the formula and x value into there as well like this

$16 = ab {}^{3}$

$4 = {ab}^{2}$

if you divide the second equation from the first

$\frac{16 = ab {}^{3} }{4 \ = ab {}^{2} }$

$4 = b {}^{}$

so our equation now is

$y = a(4) {}^{x}$

know let plug one of the point in to find a

Use 3,16

$16 = a(4) {}^{3}$

$16 = a \times 64$

$\frac{16}{64} = a$

$a = \frac{1}{4}$

So our equation is

$y = \frac{1}{4}(4) {}^{x}$