Question

A certain agency is going to use the numerals, 0 1 2 3 and the letters A and B to make tags. What is the formula for the number of tags they can make? let y be the number of tags they can make using n spaces.

Answer 1

Assuming that you can use either numerals or letters, this means that there are 6 possible choices per slot.

So if there are n slots, then there are 6^n different possible tags.

Answer 2

If the agency in the preceding problem needed to make 1296 tags, then how many spaces do they need?

Answer 3

Set 1296 equal to 6^n to get


1296 = 6^n


Now solve for n

Answer 4

N=4?

Answer 5

Good, you got it

Answer 6

Ok, what about this one:

If an agency needs to make 10000 tags, then how many numeral spaces should they use?

Answer 7

So in this part, they can only use numerals?

Answer 8

im not sure it says use the ten digits and no blank spaces. my answer choices are 5 4 3 6 7

Answer 9

well if you have 10 spaces total, and n spaces for numerals, then you'll have


4^n*2^(10-n)


possible tags


which can be simplified to


4^n*2^(10-n)

(2^2)^n*2^(10-n)

2^(2n)*2^(10-n)

2^(2n+10-n)

2^(n+10)


From here, set that equal to 10000 and solve for n

Answer 10

4?

Answer 11

yes, n = 4 is the smallest value that makes the possible number of tags exceed 10,000

Answer 12

Thank you so muchh (:

Answer 13

you're welcome