Passport to Advanced Math

Exponential Functions and Exponent Rules

Apply exponent rules and interpret exponential growth. Each question below has a complete worked solution.

This collection of 25 SAT math practice questions on exponential functions and exponent rules is sequenced by difficulty so you can warm up on routine problems and progress to the kind of question that separates a competitive math score from an elite one. The first eight problems are calibrated to roughly easy College Board difficulty — the kind that appears in the first third of the math section. The next ten are medium difficulty: the bread-and-butter of the middle of the test. The final seven push into hard territory, where the question writers add an extra step, hide a sign change, or ask for an unrelated expression after you solve.

Work each question on paper before you look at the worked solution. The solution is there to confirm or correct your work, not to lead you. If you cannot start a problem after 30 seconds, mark it and come back; if you cannot finish after 90 seconds, look at the first line of the solution and try again. That structured exposure to the worked solution — not a glance, not a copy — is the most reliable way to convert a missed question into a permanent skill.

#QuestionDifficultyBand
1 A bacteria population starts at 514 cells and multiplies by a factor of 2 every hour. How many cells… easy 400-500 Open
2 A radioactive sample of mass 751 grams loses a factor of 3 every year. What is its mass after 3 year… easy 400-500 Open
3 A bacteria population starts at 464 cells and multiplies by a factor of 5 every hour. How many cells… easy 400-500 Open
4 A radioactive sample of mass 514 grams loses a factor of 10 every year. What is its mass after 4 yea… easy 400-500 Open
5 A bacteria population starts at 265 cells and multiplies by a factor of 2 every hour. How many cells… easy 400-500 Open
6 A radioactive sample of mass 114 grams loses a factor of 3 every year. What is its mass after 2 year… easy 400-500 Open
7 A bacteria population starts at 151 cells and multiplies by a factor of 5 every hour. How many cells… easy 500-600 Open
8 A radioactive sample of mass 712 grams loses a factor of 10 every year. What is its mass after 3 yea… easy 500-600 Open
9 A bacteria population starts at 433 cells and multiplies by a factor of 2 every hour. How many cells… medium 500-600 Open
10 A radioactive sample of mass 626 grams loses a factor of 3 every year. What is its mass after 1 year… medium 500-600 Open
11 A bacteria population starts at 639 cells and multiplies by a factor of 5 every hour. How many cells… medium 500-600 Open
12 A radioactive sample of mass 755 grams loses a factor of 10 every year. What is its mass after 1 yea… medium 500-600 Open
13 A bacteria population starts at 260 cells and multiplies by a factor of 2 every hour. How many cells… medium 600-700 Open
14 A radioactive sample of mass 485 grams loses a factor of 3 every year. What is its mass after 1 year… medium 600-700 Open
15 A bacteria population starts at 696 cells and multiplies by a factor of 5 every hour. How many cells… medium 600-700 Open
16 A radioactive sample of mass 331 grams loses a factor of 10 every year. What is its mass after 1 yea… medium 600-700 Open
17 A bacteria population starts at 792 cells and multiplies by a factor of 2 every hour. How many cells… medium 600-700 Open
18 A radioactive sample of mass 874 grams loses a factor of 3 every year. What is its mass after 4 year… medium 600-700 Open
19 A bacteria population starts at 239 cells and multiplies by a factor of 5 every hour. How many cells… hard 600-700 Open
20 A radioactive sample of mass 575 grams loses a factor of 10 every year. What is its mass after 1 yea… hard 700-800 Open
21 A bacteria population starts at 540 cells and multiplies by a factor of 2 every hour. How many cells… hard 700-800 Open
22 A radioactive sample of mass 531 grams loses a factor of 3 every year. What is its mass after 3 year… hard 700-800 Open
23 A bacteria population starts at 903 cells and multiplies by a factor of 5 every hour. How many cells… hard 700-800 Open
24 A radioactive sample of mass 699 grams loses a factor of 10 every year. What is its mass after 2 yea… hard 700-800 Open
25 A bacteria population starts at 178 cells and multiplies by a factor of 2 every hour. How many cells… hard 700-800 Open