Math: 263f9937

ID: 263f9937

(SAT Suite Question Bank > Find Questions > Assessment: SAT + Test: Math + Domain: Advanced Math)

Comment: Identify the growth pattern and take things from there.

Method 1: Because the exponents are the same from Day 1 to Day 2 in the table, it is easy to compare the rate of growth: 2.5 to 5.0 doubled the number of bacteria. The pattern holds between Day 2 and Day 3, where, instead of writing 10.0 x 10^5, the exponent has changed, and, in keeping with scientific notation, the leading number goes back to a value between 1.0 (inclusive) and 10.0: 1.0 x 10^6. A little number sense can get to the answer quickly, since the leading number of our target value, 5.12 x 10^8, is a recognizable form of a power of 2.

2^1 = 2

2^2 = 4

2^3 = 8

2^4 = 16

2^5 = 32

2^6 = 64

2^7 = 128

2^8 = 256

2^9 = 512

If Day 4 would mark the first part of the chain above with the leading number of 2.0, then it stands to reason that eight days later, on Day 12, the leading digits would be 512, and 4 + 8 = 12. The correct answer is (D).

Method 2: This exponential function would grow really fast, so it might be best to use Desmos as a regular calculator, if at all. Once you spot the doubling pattern, you can simply multiply the Day 1 value by 2 and then keep changing the exponent until you got the right number.

Remembering to count Day 1 plus the other 11 days in which the number of bacteria doubled, 1 + 11 = 12, and the correct answer is (D).

Method 3: If the methods above seem like too much of a leap, you could also track each day until you reached the desired value.

Day 3: 1.0 x 10^6

Day 4: 2.0 x 10^6

Day 5: 4.0 x 10^6

Day 6: 8.0 x 10^6

Day 7: 16.0 x 10^6, or 1.6 x 10^7

Day 8: 3.2 x 10^7

Day 9: 6.4 x 10^7

Day 10: 12.8 x 10^7, or 1.28 x 10^8

Day 11: 2.56 x 10^8

Day 12: 5.12 x 10^8

The correct answer is (D).