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Sagot :
Answer:
[tex]y = \frac{1}{4} (4) {}^{x} [/tex]
Step-by-step explanation:
An exponetial function is represented by
[tex]y = ab {}^{x} [/tex]
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
[tex]16 = ab {}^{3} [/tex]
[tex]4 = {ab}^{2} [/tex]
if you divide the second equation from the first
[tex] \frac{16 = ab {}^{3} }{4 \ = ab {}^{2} } [/tex]
[tex]4 = b {}^{} [/tex]
so our equation now is
[tex]y = a(4) {}^{x} [/tex]
know let plug one of the point in to find a
Use 3,16
[tex]16 = a(4) {}^{3} [/tex]
[tex]16 = a \times 64[/tex]
[tex] \frac{16}{64} = a[/tex]
[tex]a = \frac{1}{4} [/tex]
So our equation is
[tex] y = \frac{1}{4}(4) {}^{x} [/tex]
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