Question

A population of 200 deer increases by 3% every year. Write an exponential equation that models the population, y, of deer after x years.(1 point)
The equation is $$
.
Remaining Attempts : 3

Answer 1

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

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

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

Given:
- The initial population \( P = 200 \),
- The growth rate \( r = 3\% = 0.03 \).

Substituting these values into the equation, we have:

\[
y = 200(1 + 0.03)^x
\]

Simplifying this, we get:

\[
y = 200(1.03)^x
\]

Thus, the exponential equation that models the population of deer after \( x \) years is:

\[
y = 200(1.03)^x
\]