Question

A herd of antelopes are declining at a rate of 6% a year. The herd has 570 now. After 10 years how many antelopes will be left

Answer 1

To find the number of antelopes left after 10 years, we can use the formula for exponential decay:

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

where:
- \( P(t) \) is the population after time \( t \),
- \( P_0 \) is the initial population (570 antelopes),
- \( r \) is the decay rate (6% or 0.06),
- \( t \) is the time in years (10 years).

Now, plugging in the values:

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

Calculating \( (0.94)^{10} \):

\[
(0.94)^{10} \approx 0.5220
\]

Now calculate the population after 10 years:

\[
P(10) = 570 \times 0.5220 \approx 297.54
\]

Since we can't have a fraction of an antelope, we round to the nearest whole number:

\[
P(10) \approx 298
\]

Thus, after 10 years, approximately **298 antelopes** will be left.