gailynnmoore19
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2.02 Graded Assignment: Graphing Exponential Equations
sum consumer math
will give brainliest

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?

Sagot :

MrRoyal

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

(1) How to fill the table

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

(2) The y-intercept and the rate

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

(3) The graph

See attachment for the graph of the exponential function

(4) The prices in 2000 and 2010

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

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