Question
570 elephants are declining at 6% each year. How many elephants will be left in 10 years
Answers
GPT-4o mini
To determine how many elephants will be left after 10 years with an annual decline rate of 6%, we can use the formula for exponential decay:
\[
N = N_0 \times (1 - r)^t
\]
where:
- \( N_0 \) is the initial population (570 elephants),
- \( r \) is the rate of decline (6%, or 0.06),
- \( t \) is the time in years (10 years).
Plugging in the values:
\[
N = 570 \times (1 - 0.06)^{10}
\]
\[
N = 570 \times (0.94)^{10}
\]
\[
N = 570 \times 0.5277 \quad (\text{approximately})
\]
\[
N \approx 300.39
\]
Since we cannot have a fraction of an elephant, we round this number to the nearest whole number:
\[
N \approx 300
\]
So, after 10 years, there will be approximately **300 elephants** left.
\[
N = N_0 \times (1 - r)^t
\]
where:
- \( N_0 \) is the initial population (570 elephants),
- \( r \) is the rate of decline (6%, or 0.06),
- \( t \) is the time in years (10 years).
Plugging in the values:
\[
N = 570 \times (1 - 0.06)^{10}
\]
\[
N = 570 \times (0.94)^{10}
\]
\[
N = 570 \times 0.5277 \quad (\text{approximately})
\]
\[
N \approx 300.39
\]
Since we cannot have a fraction of an elephant, we round this number to the nearest whole number:
\[
N \approx 300
\]
So, after 10 years, there will be approximately **300 elephants** left.