Questions: Let C(t) be the number of US cell phone subscribers in millions in t years since 1995. A linear model for the data is F(t) = 18.997 t + 17.711. Use the above scatter plot to decide whether the linear model fits the data well. - The function is a good model for the data. - The function is not a good model for the data. Estimate the number of subscribers in 2014. millions. Use the model to predict the year in which the number of subscribers will be 330 million.

Let C(t) be the number of US cell phone subscribers in millions in t years since 1995. A linear model for the data is F(t) = 18.997 t + 17.711. Use the above scatter plot to decide whether the linear model fits the data well. - The function is a good model for the data. - The function is not a good model for the data. Estimate the number of subscribers in 2014. millions. Use the model to predict the year in which the number of subscribers will be 330 million.
Transcript text: Let $C(t)$ be the number of US cell phone subscribers in millions in t years since 1995. A linear model for the data is $F(t)=18.997 t+17.711$. Use the above scatter plot to decide whether the linear model fits the data well. The function is a good model for the data. The function is not a good model for the data Estimate the number of subscribers in 2014. $\square$ millions Use the model to predict the year in which the number of subscribers will 330 million. $\square$
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Solution

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Solution Steps

Step 1: Determine if the linear model fits the data well
  • The scatter plot shows data points closely following a straight line.
  • The linear model \( F(t) = 18.997t + 17.711 \) appears to fit the data well.
Step 2: Estimate the number of subscribers in 2014
  • Calculate the number of years since 1995: \( 2014 - 1995 = 19 \) years.
  • Substitute \( t = 19 \) into the linear model: \[ F(19) = 18.997 \times 19 + 17.711 \] \[ F(19) = 360.943 + 17.711 = 378.654 \]
  • The estimated number of subscribers in 2014 is approximately 378.654 million.
Step 3: Predict the year when the number of subscribers will be 330 million
  • Set \( F(t) = 330 \) and solve for \( t \): \[ 330 = 18.997t + 17.711 \] \[ 330 - 17.711 = 18.997t \] \[ 312.289 = 18.997t \] \[ t = \frac{312.289}{18.997} \approx 16.44 \]
  • Add the number of years to 1995: \( 1995 + 16.44 \approx 2011.44 \).

Final Answer

  1. The function is a good model for the data.
  2. The estimated number of subscribers in 2014 is approximately 378.654 million.
  3. The model predicts that the number of subscribers will reach 330 million around the year 2011.
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