Question
In a certain geographic location, a herd of elephants is declining at a rate of four percent every
year. If there are currently 62 elephants in the herd, create an exponential decay function to model
the problem. Let y represent the number of elephants after t years. (1 point)
y = 62(0.6)
t
y = 62(1.04)
t
y = 62(0.96)
t
y = 62(0.04)
t
year. If there are currently 62 elephants in the herd, create an exponential decay function to model
the problem. Let y represent the number of elephants after t years. (1 point)
y = 62(0.6)
t
y = 62(1.04)
t
y = 62(0.96)
t
y = 62(0.04)
t
Answers
Answered by
GPT-4o mini
To create an exponential decay function for the given problem, we need to use the formula:
\[ y = y_0 \cdot (1 - r)^t \]
where:
- \( y_0 \) is the initial quantity (in this case, the initial number of elephants),
- \( r \) is the rate of decay,
- \( t \) is the time in years,
- \( (1 - r) \) represents the remaining population each year.
In your case, the initial number of elephants \( y_0 = 62 \) and the decay rate \( r = 0.04 \) (which is 4% as a decimal). Therefore, \( (1 - r) = 1 - 0.04 = 0.96 \).
Thus, the exponential decay function is:
\[ y = 62(0.96)^t \]
Among your provided options, the correct form of the function is:
\[ y = 62(0.96)^t \]
This accurately represents the decline in the elephant population over time.
\[ y = y_0 \cdot (1 - r)^t \]
where:
- \( y_0 \) is the initial quantity (in this case, the initial number of elephants),
- \( r \) is the rate of decay,
- \( t \) is the time in years,
- \( (1 - r) \) represents the remaining population each year.
In your case, the initial number of elephants \( y_0 = 62 \) and the decay rate \( r = 0.04 \) (which is 4% as a decimal). Therefore, \( (1 - r) = 1 - 0.04 = 0.96 \).
Thus, the exponential decay function is:
\[ y = 62(0.96)^t \]
Among your provided options, the correct form of the function is:
\[ y = 62(0.96)^t \]
This accurately represents the decline in the elephant population over time.