Question

a deer population in a forest starts with 100 and increases by 9% each year. write an exponential function that models the data.
y= ______

Answer 1

To model the deer population using an exponential function, you can use the formula:

\[
y = y_0 \cdot (1 + r)^t
\]

where:
- \( y \) is the population after \( t \) years,
- \( y_0 \) is the initial population,
- \( r \) is the growth rate (as a decimal),
- \( t \) is the number of years.

In this case:
- The initial population \( y_0 = 100 \),
- The growth rate \( r = 9\% = 0.09 \).

Plugging these values into the formula gives:

\[
y = 100 \cdot (1 + 0.09)^t
\]

This simplifies to:

\[
y = 100 \cdot (1.09)^t
\]

So the exponential function that models the deer population is:

\[
y = 100 \cdot (1.09)^t
\]