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)

Question

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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:

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