Question

Help me please I have a test tomorrow!

Answer 1

A. Answer: y = 32.913(1.126)ˣ

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

`(122)/(53)=b^7`

`\sqrt[7]{(122)/(53)}=b`

1.126 = b

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

53 = a(1.126)²

`(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

Explanation:

Substitute y = 500 into the equation above to solve for x:

500 = 32.913(1.126)ˣ

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