A. Answer: y = 32.913(1.126)ˣ
Step-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 = b
Substitute 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 = a
Input the a- & b-values into the general form of an exponential equation:
y = a(b)ˣ
y = 32.913(1.126)ˣ
***********************************************************************************
B. Answer: 23 minutes
Step-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]
