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

Question

Y =

Answer 1

To model the deer population with an exponential function, we can use the formula:

\[ Y = Y_0 \cdot (1 + r)^t \]

Where:

• \(Y_0\) is the initial population,
• \(r\) is the growth rate (as a decimal),
• \(t\) is the time in years,
• \(Y\) is the population after \(t\) years.

Given:

• The initial population \(Y_0 = 100\),
• The growth rate \(r = 9% = 0.09\),

We can substitute these values into the formula:

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

Simplifying further:

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

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

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