Question

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

Answer 1

To model the growth of the deer population using an exponential function, we can use the general form of an exponential growth equation:

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

where:
- \( y \) is the population at time \( t \),
- \( y_0 \) is the initial population,
- \( r \) is the growth rate (as a decimal),
- \( t \) is the time in years.

Given that the initial deer population \( y_0 \) is 100 and the growth rate \( r \) is 9% (which is 0.09 in decimal form), we can substitute these values into the equation:

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

This simplifies to:

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

Thus, the exponential function that models the deer population is:

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