Answer:
A: geometric; 4 times
B: arithmetic: 4 more
Step-by-step explanation:
An arithmetic model is a linear model, where the rate of change is constant. Growth or decay is by a constant amount from one interval to the next.
A geometric model is an exponential model, in which the rate of change is proportional to the amount. Growth or decay is by a constant factor from one interval to the next.
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A)
The equation for the sequence is given in "explicit" form:
[tex]A_n=2^{2n}[/tex]
The exponent can be split so this can be rewritten as ...
[tex]A_n=(2^2)^n=4^n[/tex]
If this were written in recursive form, it would look like ...
[tex]A_0=1,\ A_n=4\times A_{n-1}[/tex]
The fact that terms are related by a constant factor tells you the model is geometric. The factor tells you each hour the population is 4 times what it was in the previous hour.
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B)
The given equation is in "recursive" form. It tells you each term is 4 more than the previous one. This constant difference between terms means the model is arithmetic.
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Additional comment
In general, words like "more" or "increase" refer to addition, and the words "times" or "factor" refer to multiplication.
