In 1985, there were 285 cell phone subscribers in a small town. The number of subscribers increases by 75% each year until 1994. How many subscribers are there in the year 1994? (HINT: how many years is it from 1985 to 1994?)

1 answer

The number of years from 1985 to 1994 is 9 years.

To calculate the number of subscribers in 1994, we can use the formula for exponential growth. Since the number of subscribers increases by 75% each year, we can express this growth as follows:

\[ N(t) = N_0 \times (1 + r)^t \]

Where:

  • \( N(t) \) is the number of subscribers at time \( t \),
  • \( N_0 \) is the initial number of subscribers (285),
  • \( r \) is the growth rate (75% or 0.75),
  • \( t \) is the number of years (9).

Plugging in the values:

\[ N(9) = 285 \times (1 + 0.75)^9 \]

Calculating \( (1 + 0.75) \):

\[ 1 + 0.75 = 1.75 \]

Now raise 1.75 to the power of 9:

\[ 1.75^9 \approx 33.4132 \]

Now multiply by the initial number of subscribers:

\[ N(9) = 285 \times 33.4132 \approx 9512.282 \]

Rounding to the nearest whole number, the estimated number of subscribers in 1994 is approximately:

\[ \boxed{9512} \]