The tick marks on the number line shown are equally spaced. What is

The tick marks on the number line shown are equally spaced. What is the value of n?

We see that there is one unit between \(4^7\) and \(4^9\) and two units between \(4^9\) and \(n\).

So, since we are given that "The tick marks on the number line shown are equally spaced," the difference between \(4^9\) and \(n\) will be twice the difference between \(4^7\) and \(4^9\).

Accordingly, the value of \(n\) will be \(4^7 +\) three times the difference between \(4^7\) and \(4^9\).

The difference between \(4^7\) and \(4^9\) is the following:

\(4^9 - 4^7 = (4^2)(4^7) - 4^7 = 16(4^7) - 4^7 = 15(4^7)\)

So, each unit between two tick marks is \(15(4^7)\).

Thus, \( n = 4^7 + 3(15(4^7)) = 4^7 + 45(4^7) = 46(4^7)\).

A. \(4^{11}\)
B. \(4^{13}\)
C. \(30(4^7)\)
D. \(31(4^7)\)
E. \(46(4^7)\)

Now, to get the question correct, we must be sure to answer the question asked.

(C) is a trap choice that is the difference between \(4^9\) and \(n\).

(D) is a trap choice that is \(4^7 +\) the difference between \(4^9\) and \(n\).

Correct answer: