PSAT Math Multiple-Choice Question 636: Answer and Explanation

Question: 636

The table below gives the number of computers infected with a virus. Which of the following functions models the number of computers infected, C(d), after d days?

Spread of a Computer Virus

Day	Number of Computers Infected
1	101
2	110
3	200
4	1,100
5	10,100

• A. C(d) = 10^2d + 10(d - 1) + 1
• B. C(d) = 100 + 10^d
• C. C(d) = 100 + 10(d - 1) + 1
• D. C(d) = 100 + 10^{(d - 1)}

Correct Answer: D

Explanation:

(D) The easiest way to approach a problem like this is to test some points with each equation to see which equation works.

Choice (A):

C(1) = 10²⁽¹⁾ + 10(1 - 1) + 1 = 100 + 1 = 101

So the equation works for day 1. Let's see if it works with day 2:

C(2) = 10²⁽²⁾ + 10(2 - 1) + 1 = 10,000 + 10 + 1 = 10,011

This doesn't match the number for day 2, so we can rule out choice (A).

Choice (B):

C(1) = 100 + 10¹ = 100 + 10 = 110

This isn't the right number for day 1, so we can rule out choice (B).

Choice (C):

C(1) = 100 + 10(1 - 1) + 1 = 100 + 1 = 101

This works, so let's try C(2):

C(2) = 100 + 10(2 - 1) + 1 = 100 + 10 + 1 = 111

This doesn't work, so we can rule out choice (C).

Choice (D):

C(1) = 100 + 10^{1 - 1} = 100 + 1 = 101

C(2) = 100 + 10^{2 - 1} = 100 + 10 = 110

C(3) = 100 + 10^{3 -1} = 100 + 100 = 200

C(4) = 100 + 10^{4 - 1} = 100 + 1,000 = 1,100

C(5) = 100 + 10^{5 - 1} = 100 + 10,000 = 10,100

Obviously, choice (D) is the correct answer.