Question

5.Convert the recursive form a1=5, an=2an−1
to the explicit form. (1 point)
Responses

an=2(5)n−1

A sub n is equal to 2 times 5 raised to the n minus 1 power

an=5(2)n+1

A sub n is equal to 5 times 2 raised to the n plus 1 power

an=5(2)n−1

A sub n is equal to 5 times 2 raised to the n minus 1 power

an=3(7)n
4.The population of bunnies in March is 12. A researcher notices that the population is tripling each month. The population can be represented by the equation P = 12(3)x
where x is the number of months since March. What will the population of bunnies be after 5 months? (1 point)
Responses

420
420

2916
2916

243
243

180
3.Which of the following is UNLIKE the others with respect to the rate of change (common difference)?(1 point)
Responses

an = −5 + 6(n − 1)

an = −5 + 6(n − 1)


2, 8, 12, 20, 26

2, 8, 12, 20, 26


f(x) = 6x − 2

f(x) = 6x − 2


f(x) = 6x +1
2.(6 points)
Compare the linear function and the arithmetic sequence below.

Linear Function:

x y
-1 10
0 14
1 18
2 22

The rate of change of the linear function is

The y-intercept of the linear function is

Arithmetic Sequence (Explicit formula):

an = 10+ 4(n−1)


The rate of change (common difference) of the arithmetic sequence is

The first value of the arithmetic sequence is

The rate of change of this linear function is
the rate of change of this arithmetic sequence.

Arithmetic sequences
can be represented as a linear function.

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1.A car has 121,358 miles on its odometer and accumulates an average of 255 more each week. What is the function rule that represents the total number of M miles the car will have on the odometer after w weeks? (1 point)
Responses

M(w)=121,358+255

cap m times w is equal to 121 comma 358 plus 255

M(w)=121,358+255w

cap m times w is equal to 121 comma 358 plus 255 w

M(w)=121,358w+255

cap m times w is equal to 121 comma 358 w plus 255

M(w)=121,358w+255w

cap m times w is equal to 121 comma 358 w plus 255 w

Answer 1

Here are the answers:

5. Recursive a1 = 5, an = 2·an−1 -> explicit: an = 5(2)^(n−1).

4. Bunny population after 5 months: 12·3^5 = 2916.

3. UNLIKE the others (different common difference): 2, 8, 12, 20, 26.

2. Linear function table:
- Rate of change = 4
- y-intercept = 14

Arithmetic sequence an = 10 + 4(n−1):
- Common difference = 4
- First term = 10

The rate of change of the linear function is equal to the rate of change of the arithmetic sequence.
Arithmetic sequences can be represented as linear functions.

1. Odometer function: M(w) = 121,358 + 255w.