Since

, we know that

follows a Poisson distribution with parameter

.
Now assuming

denote the mean and standard deviation of

, respectively, then we know right away that

and

.
So,
Since the variable x is at the exponent, this is an exponential function.
To decide whether an exponential function is a growing or decaying one, we have to look at the base of the exponent.
If the base is between 0 and 1, we have exponential decay
If the base is larger than 1, we have exponential growth.
In your case the base is 3, which is larger than 1, so you have exponential growth.
Thus, <u>option d</u> is your answer
Step-by-step explanation:
Center: (−7,4)(-7,4)
Radius: 7
The rate of change is 4. A linear model.