Question

Mlekete owns a small business that currently has 254 clients. The number of clients is expected to grow by 2.3% each year.
Write an exponential function to model the number of clients, y, after x years.

y=__

Answer 1

y=

Answer 2

To model the number of clients \( y \) after \( x \) years with an initial number of clients \( P = 254 \) and a growth rate of \( r = 2.3\% = 0.023 \), you can use the formula for exponential growth:

\[
y = P \cdot (1 + r)^x
\]

Substituting the values into the equation, we have:

\[
y = 254 \cdot (1 + 0.023)^x
\]

This simplifies to:

\[
y = 254 \cdot (1.023)^x
\]

Therefore, the exponential function that models the number of clients after \( x \) years is:

\[
y = 254 \cdot (1.023)^x
\]

Answer 3

The exponential function that models the number of clients \( y \) after \( x \) years is:

\[
y = 254 \cdot (1.023)^x
\]

This equation shows that the number of clients will grow exponentially at a rate of 2.3% per year, starting from 254 clients.