To determine the number of cell phone subscribers in Glenwood in 1990 given that there were 285 subscribers in 1985 and the number of subscribers increased by 75% per year, let's follow a detailed step-by-step approach:
1. Understand the Growth Rate: The number of subscribers increases by 75% each year. This means each year the number of subscribers is multiplied by [tex]\(1 + 0.75 = 1.75\)[/tex].
2. Calculate the Number of Subscribers Each Year:
- From 1985 to 1986 (1 year):
[tex]\( 285 \times 1.75 = 498.75 \)[/tex]
- From 1986 to 1987 (2 years):
[tex]\( 498.75 \times 1.75 = 872.8125 \)[/tex]
- From 1987 to 1988 (3 years):
[tex]\( 872.8125 \times 1.75 = 1527.421875 \)[/tex]
- From 1988 to 1989 (4 years):
[tex]\( 1527.421875 \times 1.75 = 2672.98828125 \)[/tex]
- From 1989 to 1990 (5 years):
[tex]\( 2672.98828125 \times 1.75 = 4677.7294921875 \)[/tex]
3. Results and Intermediate Calculations:
- The number of subscribers in 1986 is approximately 498.75, which we can round to 498.
- The number of subscribers in 1987 is approximately 872.8125, which we can round to 872.
- The number of subscribers in 1988 is approximately 1527.421875, which we can round to 1527.
- The number of subscribers in 1989 is approximately 2672.98828125, which we can round to 2672.
- The number of subscribers in 1990 is approximately 4677.7294921875, which we can round to 4677.
Thus, the number of cell phone subscribers in Glenwood in 1990 is 4677.
From the provided multiple-choice options, the correct answer is:
d. 4677.
