Answer:
One
Step-by-step explanation:
General form of an exponential function: [tex]y=ab^x[/tex]
where a is the initial value, b is the growth/decay factor, and x is the independent variable
If b > 1 the function will grow (increase). If 0 < b < 1 then the function will decay (decrease)
The value Kaylee found is not the constant ratio of successive values. She should use ordered pairs with x-values that differ by 1
This is how Kaylee computed the value of b, which was incorrect as the solution of 8 is for [tex]b^2[/tex]:
at (1, 6): [tex]ab^1=6[/tex]
at (3, 48) [tex]ab^3=48[/tex]
[tex]\implies \dfrac{ab^3}{ab^1}=\dfrac{48}{6}\\\\\implies b^2=8\\\\\implies b=\pm\sqrt{8} =2\sqrt{2}[/tex]
(b is positive since the function is increasing)
However, if Kaylee used the ordered pairs with a difference of one, e.g. x = 1 and x = 2, then she would have computed the correct value of b:
at (1, 6): [tex]ab^1=6[/tex]
at x = 2: [tex]ab^2=y[/tex]
[tex]\implies \dfrac{ab^2}{ab^1}=\dfrac{y}{6}\\\\\implies b=\dfrac{y}{6}[/tex]
