Question

Help me please I have a test tomorrow!

Answer 1

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    

                                    $\dfrac{122}{53}=b^7$

                                    $\sqrt[7]{\dfrac{122}{53}}=b$

                                    1.126 = b

Substitute the b-value into either of the equations to solve for "a":

53 = a(1.126)²

$\dfrac{53}{(1.126)^2}=a$

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

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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

$\dfrac{500}{32.913}=(1.126)^x\\\\\\ln\bigg(\dfrac{500}{32.913}\bigg)=ln(1.126)^x\\\\\\ln\bigg(\dfrac{500}{32.913}\bigg)=x\cdot ln(1.126)\\\\\\\dfrac{ln\bigg(\dfrac{500}{32.913}\bigg)}{ln(1.126)}=x\\\\\\\boxed{23 = x}$