A. Answer: y = 32.913(1.126)ˣStep-by-step explanation:You are given two coordinates (2, 53) and (9, 122). Use these to create a system of equations:53 = a(b)² and 122 = a(b)⁹ 122 = a(b)²· (b)⁷ 122 = 53 · (b)⁷ [tex]\dfrac{122}{53}=b^7[/tex] [tex]\sqrt[7]{\dfrac{122}{53}}=b[/tex] 1.126 = bSubstitute the b-value into either of the equations to solve for "a":53 = a(1.126)²[tex]\dfrac{53}{(1.126)^2}=a[/tex]32.913 = aInput the a- & b-values into the general form of an exponential equation:y = a(b)ˣy = 32.913(1.126)ˣ***********************************************************************************B. Answer: 23 minutesStep-by-step explanation:Substitute y = 500 into the equation above to solve for x:500 = 32.913(1.126)ˣ[tex]\dfrac{500}{32.913}=(1.126)^x\\\\\\ln\bigg(\dfrac{500}{32.913}\bigg)=ln(1.126)^x\\\\\\ln\bigg(\dfrac{500}{32.913}\bigg)=x\cdot ln(1.126)\\\\\\\dfrac{ln\bigg(\dfrac{500}{32.913}\bigg)}{ln(1.126)}=x\\\\\\\boxed{23 = x}[/tex]