Question

I don’t know if I’m right

Answer 1

A: geometric; 4 times

B: arithmetic: 4 more

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:

`A_n=2^(2n)`

The exponent can be split so this can be rewritten as ...

`A_n=(2^2)^n=4^n`

If this were written in recursive form, it would look like ...

`A_0=1,\ A_n=4* A_(n-1)`

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.