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)
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
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
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
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
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
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
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
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?