2.02 Graded Assignment: Graphing Exponential Equations
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1. We mentioned how the price of movie tickets has increased over time with inflation in Unit 6. Let’s let the equation y = 0.50(1.06)x represent the price of movie tickets for the years after 1950.
Using this equation, fill in the following T-table for the years 1950, 1960, 1970, 1980, and 1990. Use X = 0, 10, 20, 30, and 40 to represent these years (the number of years after 1950).

# years after 1950 X
Ticket Price $ Y

2. Answer these questions:
• Do these prices look reasonable?
• What is the y-intercept?
• Is this growth or decay?

3. Graph the points on the graph provided and draw a smooth curve to represent the graph of the equation.

4. Use the extended curve below to predict the ticket prices in the following years:
• 2000 (x = 50)
• 2010 (x = 60)
• Are these prices reasonable?

5. Answer these questions:
• What is the average price of a movie ticket where you live?
• What is the price of a matinee?
• Substitute the number of years after 1950 that it is right now into the equation y = 0.50(1.06)x. (For instance, if it is 2006, use x = 56.) What answer did you get?
• Why do you think this is the same or different from the first answer you gave in this question?

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MrRoyal MrRoyal · Answer 1 · 2022-02-11T07:08:18+01:00

An exponential function is a function that has the form y = ab^x, where a represents the initial value, and b represents the rate

The exponential function is given as:

[tex]y = 0.50(1.06)^x[/tex]

When x = 0, we have:

[tex]y = 0.50 * (1.06)^0 = 0.50[/tex]

When x = 10, we have:

[tex]y = 0.50 * (1.06)^{10} = 0.90[/tex]

When x = 20, 30 and 40 we have:

[tex]y = 0.50 * (1.06)^{20} = 1.60[/tex]

[tex]y = 0.50 * (1.06)^{30} = 2.87[/tex]

[tex]y = 0.50 * (1.06)^{40} = 5.14[/tex]

So, the complete table is:

Years after 1950 X : 0 | 10 | 20 | 30 | 40

Ticket Price $ Y : 0.50 | 0.90 | 1.60 | 2.87 | 5.14

The prices look reasonable.

The y-intercept is when x = 0.

So, the value of the y-intercept is 0.50

Also, the rate represents a growth.

This is so, because the rate is greater than 1

See attachment for the graph of the exponential function

When x = 50 and 60, we have:

[tex]y = 0.50 * (1.06)^{50} = 9.21[/tex]

[tex]y = 0.50 * (1.06)^60} = 16.49[/tex]

Hence, the prices in 2000 and 2010 are $9.21 and $16.49

Read more about exponential functions at:

https://brainly.com/question/11464095