Question

) In a certain geographic location, a herd of antelopes is declining at a rate of six percent every
year. If there are currently 570 antelopes in the herd, create an exponential decay function to
model the problem. If the decrease in population continues at this rate, how many antelopes will
be in the herd after 10 years? Round your answer to the nearest whole number.
After 10 years there will be antelopes

Answer 1

To create an exponential decay function for the antelope population, we can use the formula:

\[
P(t) = P_0 \times (1 - r)^t
\]

Where:
- \( P(t) \) is the population after \( t \) years,
- \( P_0 \) is the initial population,
- \( r \) is the decay rate (as a decimal),
- \( t \) is the time in years.

Given:
- \( P_0 = 570 \) (current population),
- \( r = 0.06 \) (6% decline per year),
- \( t = 10 \) years.

Substituting the values into the formula, we have:

\[
P(10) = 570 \times (1 - 0.06)^{10}
\]
\[
P(10) = 570 \times (0.94)^{10}
\]

Now, we need to calculate \( (0.94)^{10} \):

\[
(0.94)^{10} \approx 0.527
\]

Now substitute back into the equation:

\[
P(10) = 570 \times 0.527 \approx 300.39
\]

Rounding to the nearest whole number:

\[
P(10) \approx 300
\]

Thus, after 10 years, there will be approximately **300** antelopes in the herd.