Question

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?)

Answer 1

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:

\[
\boxed{9512}
\]