9514 1404 393
Answer:
y = 4.78(1.71)^x
Step-by-step explanation:
Put the given values into the given formula and solve the two equations for the two unknowns.
[tex]y=a(b)^x\\\\14=a(b)^2\\\\205=a(b)^7\\\\\textsf{Divide the second equation by the first}\\\\\dfrac{205}{14}=\dfrac{a(b)^7}{a(b)^2}=b^5\\\\b=\sqrt[5]{\dfrac{205}{14}}\approx 1.71\qquad\text{fifth root}\\\\a=\dfrac{14}{b^2}\qquad\text{first equation solved for $a$}\\\\a=14\sqrt[5]{\left(\dfrac{14}{205}\right)^2}\approx 4.78\qquad\text{substitute for b}[/tex]
So, the approximate equation is ...
y = 4.78(1.71)^x
_____
A graph shows the points fall very close to the curve.
