Question

Exponential Decay Quick Check
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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)
Responses

y=62(0.6)t
y equals 62 left parenthesis 0.6 right parenthesis superscript t baseline

y=62(0.96)t
y equals 62 left parenthesis 0.96 right parenthesis superscript t baseline

y=62(0.04)t
y equals 62 left parenthesis 0.04 right parenthesis superscript t baseline

y=62(1.04)t

Answer 1

To create an exponential decay function to model the population of elephants declining at a rate of 4% per year, we can start with the initial number of elephants, which is 62.

Since the herd is declining at a rate of 4%, the remaining population after one year will be 96% of the current population. This is calculated as follows:

1 - decay rate = 1 - 0.04 = 0.96.

The exponential decay function can be expressed as:

\[ y = y_0 \cdot (1 - r)^t \]

where:
- \( y_0 \) is the initial amount (62 elephants),
- \( r \) is the decay rate (0.04), and
- \( t \) is the number of time periods (years).

Substituting in our values, we get:

\[ y = 62 \cdot (0.96)^t \]

So the correct response is:

**y = 62(0.96)^t**

y equals 62 left parenthesis 0.96 right parenthesis superscript t baseline.