To determine the equation that models the number of cell phone subscribers in the city each year after 2000, we need to understand the nature of the growth described in the problem.
Here's the process step-by-step:
1. Identify the Initial Value:
- In the year 2000, the initial number of subscribers is 200,000.
2. Identify the Growth Rate:
- The number of subscribers increases by 60% per year. This can be represented as a decimal by converting 60% to 0.6.
3. Choose the Appropriate Growth Formula:
- The general formula for exponential growth is [tex]\( y = A(1 + r)^t \)[/tex]:
- [tex]\( A \)[/tex] is the initial amount.
- [tex]\( r \)[/tex] is the growth rate.
- [tex]\( t \)[/tex] is the number of years after the initial time period.
- [tex]\( y \)[/tex] is the amount after [tex]\( t \)[/tex] years.
4. Substitute Values into the Formula:
- Here, [tex]\( A = 200,000 \)[/tex], [tex]\( r = 0.6 \)[/tex], and [tex]\( t \)[/tex] is the number of years after 2000.
- Substituting these values into the formula gives us:
[tex]\[
y = 200,000(1 + 0.6)^t
\][/tex]
5. Select the Correct Option:
- Option B. [tex]\( y = 200,000(1 + 0.6)^t \)[/tex] correctly models the exponential growth described.
Therefore, the correct equation to model the number of subscribers [tex]\( y \)[/tex] in the city [tex]\( t \)[/tex] years after 2000 is:
[tex]\[
\boxed{y = 200,000(1 + 0.6)^t}
\][/tex]
Thus, the correct answer is option B.
