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In a particular country, the average adult is spending even more time on a mobile device than watching television. From 2014 to 2021,
the function y = - 7.12x + 260 can be used to estimate the average number of minutes per day that an adult spends
watching television, and the function y = 12.87x + 157.8 can be used to estimate the average number of minutes per day that an adul
spends on a mobile device. For both functions, x is the number of years after 2014.
a. Based on this information, determine the year in which the time spent watching television is the same as the fime spent on a mobile device.
b. Use these functions to predict how much time the average adult spends per day watching television and on a mobile device for the year 2021.

We are given two linear functions that describe the average number of minutes per day that an adult spends watching television and on a mobile device. The functions are as follows:

- Time spent watching television: \( y_{\text{tv}} = -7.12x + 260 \)
- Time spent on a mobile device: \( y_{\text{mobile}} = 12.87x + 157.8 \)

Where:
- \( x \) is the number of years after 2014.
- \( y \) represents the number of minutes spent.

### Part (a): Determine the year when time spent on television equals time spent on mobile devices

To find when the time spent on watching television equals the time spent on mobile devices, we need to set the two functions equal to each other and solve for \( x \):

\[
-7.12x + 260 = 12.87x + 157.8
\]

Now let's solve for \( x \).

### Part (b): Predict time spent in 2021

For 2021, \( x = 2021 - 2014 = 7 \). We will substitute \( x = 7 \) into both functions to find the time spent watching television and on mobile devices in 2021.

Let's calculate both parts.### Part (a): Year when time spent on television equals time spent on mobile devices
The time spent on television and mobile devices will be the same approximately **5.11 years** after 2014. This corresponds to the year:

\[
2014 + 5.11 \approx 2019
\]

So, in **2019**, the time spent watching television and using a mobile device was the same.

### Part (b): Time spent in 2021
In 2021 (\(x = 7\)):
- The average adult spent approximately **210.16 minutes** per day watching television.
- The average adult spent approximately **247.89 minutes** per day on a mobile device.

Would you like further details on these calculations or have any questions?

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Here are some related questions:
1. How would the trends change if the coefficients were slightly altered?
2. What would the time difference be if the functions were extended to 2025?
3. How many years after 2021 would mobile usage exceed television by a certain margin?
4. How does the slope of each function reflect changes in behavior?
5. Can we use this data to estimate future device usage in other regions?

**Tip:** Always double-check calculations when working with linear functions to ensure precise results!

In a particular country, the average adult is spending even more time on a mobile device than watching television. From 2014 to 2021, the function y = - 7.12x + 260 can be used to estimate the average number of minutes per day that an adult spends watching television, and the function y = 12.87x + 157.8 can be used to estimate the average number of minutes per day that an adult spends on a mobile device. For both functions, x is the number of years after 2014. a. Based on this information, determine the year in which the time spent watching television is the same as the time spent on a mobile device. b. Use these functions to predict how much time the average adult spends per day watching television and on a mobile device for the year 2021.

Explore how linear equations can be used to estimate the time spent watching television and using mobile devices between 2014 and 2021. This problem calculates when the time spent on both activities was equal and predicts the values for 2021. Suitable for high school students studying algebra and linear equations.

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