Questions and Answers
The function f(x) = 2(3.2)^x increases at a constant multiplicative rate.
True
What is the multiplicative rate of change for the exponential function graphed to the left?
3
Which graph represents the function f(x) = 3/2(2)^x?
How will the appearance of the graph change if the a value in the function f(x) = 2(5)^x is decreased but remains greater than 0?
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What values should Jemel use for a and b in the function f(x) = ab^x to represent 240 birds increasing at a rate of 16% annually?
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If Leticia invests $200 at 5% interest, what describes the graph of the exponential function related to time and money?
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What function represents a population of 1500 bacteria increasing at a rate of 115% each hour?
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What happens to the function if the base of the exponent is 1?
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At 10:05 a.m., there are 2 microscopic bacteria cells. How many cells will be in the bottle at 10:15 a.m.?
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At what time will there be 16 cells in the bottle?
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At what time will the bottle be 1/2 full if it is 1/4 full at 11:30 a.m.?
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What fraction of the bottle was full at 11:20 a.m. if the bacteria is doubling every five minutes?
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What does the ordered pair (15, 8) represent in the exponential growth of bacteria?
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If the cells continue to double every 5 minutes, how long will it take to fill 3 additional bottles of the same size?
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Explain how the bacteria took 1 hour and 40 minutes to fill the initial bottle but only took 10 minutes to fill 3 additional bottles.
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Study Notes
Exponential Growth Functions
- The function f(x) = 2(3.2)^x increases at a constant multiplicative rate.
- The multiplicative rate of change for certain exponential functions can be determined; for example, it is 3 for one specific graph.
- The graph corresponding to f(x) = (3/2)(2)^x is represented as Graph 4.
- If the 'a' value in the function f(x) = 2(5)^x is decreased (but remains positive), the graph will start lower on the y-axis.
- The function f(x) = 3(2.5)^x is exponential and increases by a multiplicative factor of 2.5 for each unit increase in x. Its domain is all real numbers.
- For a population of 240 birds with an annual growth rate of 16%, the initial value (a) is 240 and the growth factor (b) is 1.16 when modeled by f(x) = ab^x.
- Leticia’s investment of $200 at 5% interest grows, starting from 200 and increasing by a factor of 1.05 for each time unit.
- A colony of 1500 bacteria grows at a rate of 115% per hour, modeled by f(x) = 1500(2.15)^x.
- When the base of an exponential function is exactly 1, the output remains constant, resulting in a horizontal line on a graph. A base between 0 and 1 leads to a decreasing function.
- Starting with 2 bacteria, the count reaches 8 by 10:15 a.m.; extrapolating leads to 16 cells by 10:20 a.m. and 64 cells by 10:30 a.m.
- At 11:30 a.m., the bottle is 1/4 full; it will reach 1/2 full by 11:35 a.m.
- By 11:40 a.m., the bottle is full, confirmed by the observations that each doubling takes place every 5 minutes (1/2 full at 11:35 a.m., 1/4 full at 11:30 a.m.).
- At 11:20 a.m., the bottle contained 1/16 of its capacity due to the doubling time of the bacteria.
- The ordered pair (15, 8) represents that there are 8 bacteria cells after 15 minutes.
- If bacteria continue doubling every 5 minutes, it will take 10 minutes to fill three additional bottles of the same size.
- The bacteria took 1 hour and 40 minutes to fill the first bottle. Once full, each bacterium multiplied rapidly, filling additional bottles much quicker—5 minutes per bottle once the initial is full.
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Description
Test your knowledge of exponential growth functions with this set of flashcards. Answer questions related to tables, multiplicative rates, and graph representations of exponential functions. Ideal for students looking to reinforce their understanding of the material.
