Question

use the equation for the line of best fit to predict the price of a ticket in 2020? $33.80 if the trend continues in what year will the price of the tickets hit $57?

Explanation:

Step1: Find \(x\) for 2020

The \(x\) - value represents the years since 2000. For 2020, \(x = 2020 - 2000=20\).

Step2: Substitute \(x = 20\) into \(f(x)=1.04x + 13\)

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Step3: Solve for \(x\) when \(f(x) = 57\)

Set \(1.04x+13 = 57\). First, subtract 13 from both sides: \(1.04x=57 - 13=44\). Then divide both sides by 1.04: \(x=\frac{44}{1.04}\approx42.31\).

Step4: Find the year

Since \(x\) is the number of years since 2000, the year is \(2000 + 42.31\approx2042\)

Answer:

The price of a ticket in 2020 is \(\$33.8\). If the trend continues, the price of the tickets will hit \(\$57\) in approximately the year \(2042\)