Question

Denise collects stuffed animals. The number of stuffed animals in her collection, a, after n, number of years, can be described by the equation a(n) = 3 + 4n. Which statement best describes the rate of change?

A. The number of stuffed animals in Denise’s collection is multiplied by 4 each year.
B. Denise’s collection increases by 4 stuffed animals per year.
C. Denise’s collection increases by 3 stuffed animals per year.
D. Denise spends $4 per year on stuffed animals.

Answer 1

I think the answer would be A

Answer 2

The statement best describes the rate of change is "Denise's collection increases by 4  stuffed animals each year".

What is rate of change ?

The rate of change is the speed at which a variable changes over a specific period of time.

According to the given question

We have

An equation a(n) = 3+4n, which describes the number of stuffed animal in Denise collection, a after n, number of years.

For the rate of change

Differentiate the given equation w.r.t n

⇒$\frac{d(a(n))}{dn} =\frac{d}{dn} (3) + \frac{d}{dn} (4n)$

⇒$\frac{d}{dn} a(n) = 0+ 4 =4$

⇒ the number of stuffed collection increases by 4 each year.

Hence, option B is correct.

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