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)

Question

Responses

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

y=62(1.04)t
y equals 62 left parenthesis 1.04 right parenthesis superscript t baseline

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

y=62(0.6)t

Answer 1

To model the decline of the elephant herd, we can use an exponential decay function of the form:

$$y=y_0\cdot (1-r{)}^t$$

where:

• $y_0$ is the initial quantity (in this case, 62 elephants),
• $r$ is the decay rate (in this case, 4%, which is 0.04 in decimal form),
• $t$ is the time in years.

Since the herd is declining by 4% each year, we can express $(1-r)$ as $(1-0.04)=0.96$.

Thus, the exponential decay function becomes:

$$y=62\cdot (0.96{)}^t$$

Therefore, the correct response is:

$$y=62(0.96{)}^t$$

So the answer is:

y = 62(0.96)^t