Mr. Kone Math Hub · Review sheet

Exponential Growth and Decay

Unit 10: Exponential Functions · AI-F.LE.1, AI-F.LE.2

Algebra I Regents

Notes

The multiplier. Increase by 6% → multiply by 1.06. Decrease by 15% → multiply by 0.85. The general form is y = a · b^x, where a is the starting value.

Vocabulary

  • exponential function: A function with constant multiplicative rate of change, often y = a·b^x.

Practice (no calculator unless marked)

  1. Mike uses the equation b = 1300(2.65)ˣ to determine the growth of bacteria in a laboratory setting. The exponent represents
    • A. the total number of bacteria currently present
    • B. the percent at which the bacteria are growing
    • C. the initial amount of bacteria
    • D. the number of time periods
  2. On an island, a rare breed of rabbit doubled its population each month for two years. Which type of function best models the increase in population at the end of two years?
    • A. linear growth
    • B. linear decay
    • C. exponential growth
    • D. exponential decay
  3. The third term in a sequence is 25 and the fifth term is 625. Which number could be the common ratio of the sequence?
    • A. 1/5
    • B. 5
    • C. 1/25
    • D. 25
  4. Mike uses the equation b = 1300(2.65)ˣ to determine the growth of bacteria in a laboratory setting. The exponent represents
    • A. the total number of bacteria currently present
    • B. the percent at which the bacteria are growing
    • C. the initial amount of bacteria
    • D. the number of time periods
  5. On an island, a rare breed of rabbit doubled its population each month for two years. Which type of function best models the increase in population at the end of two years?
    • A. linear growth
    • B. linear decay
    • C. exponential growth
    • D. exponential decay
  6. The third term in a sequence is 25 and the fifth term is 625. Which number could be the common ratio of the sequence?
    • A. 1/5
    • B. 5
    • C. 1/25
    • D. 25
  7. Mike uses the equation b = 1300(2.65)ˣ to determine the growth of bacteria in a laboratory setting. The exponent represents
    • A. the total number of bacteria currently present
    • B. the percent at which the bacteria are growing
    • C. the initial amount of bacteria
    • D. the number of time periods
  8. On an island, a rare breed of rabbit doubled its population each month for two years. Which type of function best models the increase in population at the end of two years?
    • A. linear growth
    • B. linear decay
    • C. exponential growth
    • D. exponential decay