Suppose the number of mobile-phone subscribers (in millions) between 1995 and 2006 can be modeled by Upper S left parenthesis x right parenthesis equals 18.31 x plus 20.93, where x is the number of years after 1995. In what year does this model indicate that there were 332 comma 200 comma 000 subscribers?

Question

Suppose the number of​ mobile-phone subscribers​ (in millions) between 1995 and 2006 can be modeled by Upper S left parenthesis x right parenthesis equals 18.31 x plus 20.93​, where x is the number of years after 1995. In what year does this model indicate that there were 332 comma 200 comma 000 ​subscribers?

GPT-4o mini · Answer

To find the year when the number of mobile-phone subscribers reached 332,200,000, we need to first express that quantity in millions (since the model \( S(x) \) is given in millions).

332,200,000 subscribers in millions is: \[ \frac{332,200,000}{1,000,000} = 332.2 \text{ million} \]

Now, we can set the function equal to 332.2 million: \[ S(x) = 18.31x + 20.93 \] \[ 332.2 = 18.31x + 20.93 \]

Next, we need to solve for \( x \). First, isolate \( 18.31x \): \[ 332.2 - 20.93 = 18.31x \] \[ 311.27 = 18.31x \]

Now, divide both sides by 18.31 to find \( x \): \[ x = \frac{311.27}{18.31} \approx 17.016 \]

Since \( x \) represents the number of years after 1995, we will round \( x \) to the nearest whole number: \[ x \approx 17 \]

Thus, if \( x = 17 \), we find the year: \[ 1995 + 17 = 2012 \]

So, based on this model, the year when there were approximately 332,200,000 subscribers is \( \text{2012} \).