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指数增长・衰减与复利挑战
In a computer application, the area of a figure on the screen increases over time. This area, in pixels, is given by the function \( A(t)=16(2)^t \), where t is the number of seconds after the area of the figure begins increasing. Which statement is the best interpretation of A(7)=2,048 in this context?
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指数增长・衰减与复利进阶
A scientist initially measures 9,000 bacteria in a growth medium. 8 hours later, the scientist measures 18,000 bacteria. Assuming exponential growth, the formula \( P=C(2)^{rt} \)gives the number of bacteria in the growth medium, where r and C are constants and P is the number of bacteria t hours after the initial measurement. What is the value of r?
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指数增长・衰减与复利进阶
For a certain isotope, at the end of every 29-year period, the mass of a sample of the isotope has decayed to half its mass at the beginning of the 29-year period. The function \( s(t)=264(0.5)^{\frac{t}{29}} \) gives the approximate mass of this isotope, in grams, that remains t years after a 264-gram sample starts to decay. Which statement is the best interpretation of \( s(3·29)=33 \) in this context?
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指数增长・衰减与复利挑战
The function \( f(n)=7(20.59)^{\frac{n}{4}} \) gives each term of a sequence as a function of the term’s position, n, in the sequence, where n is a whole number. The value of the term in position 14 is p% more than the value of the term in position 10. What is the value of p?
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指数增长・衰减与复利进阶
For a certain isotope, at the end of every 29-year period, the mass of a sample of the isotope has decayed to half its mass at the beginning of the 29-year period. The function \( s(t)=192(0.5)^{\frac{t}{29}} \) gives the approximate mass of this isotope, in grams, that remains t years after a 192-gram sample starts to decay. Which statement is the best interpretation of \( s(2·29)=48 \) in this context?
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指数增长・衰减与复利挑战
The function \( f(n)=7(20.43)^{\frac{n}{5}} \) gives each term of a sequence as a function of the term's position, n, in the sequence, where n is a whole number. The value of the term in position 15 is p% more than the value of the term in position 10. What is the value of p?
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指数增长・衰减与复利挑战
\( f(x)=2,000(0.80)^x \)
A conservation scientist implemented a program to reduce a certain invasive insect population in an area. The given function estimates this insect species' population x years after 2008, where \( x\le8 \). Which of the following is the best interpretation of 2,000 in this context?
A conservation scientist implemented a program to reduce a certain invasive insect population in an area. The given function estimates this insect species' population x years after 2008, where \( x\le8 \). Which of the following is the best interpretation of 2,000 in this context?
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指数增长・衰减与复利进阶
The function \( f(x)=230,000(1.23)^x \) gives a company’s predicted annual revenue, in dollars, x years after the company started selling clothes online, where \( 0<x≤10 \). What is the best interpretation of the statement “\( f(6) \) is approximately equal to 796,450” in this context?
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指数增长・衰减与复利基础
The graph shows the estimated concentration of a certain strain of bacteria, in millions of cells per mL of nutrient medium, over time x, in minutes since the initial measurement. According to the graph, which of the following is closest to the number of minutes it took for the estimated concentration of the bacteria to increase from the initial concentration to 20 million cells per mL of nutrient medium?
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指数增长・衰减与复利基础
A fully charged battery has an initial charge of 100 units. When this battery is in use, the remaining charge of the battery at any given moment is approximately 80% of the charge from one hour earlier. Which function \( f \) gives the approximate remaining charge, in units, of this battery when it is in use for x hours?
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指数增长・衰减与复利挑战
The equation \( N(m)=64(Q)^{\frac{m}{6}} \) gives the predicted population N(m), in thousands, of a certain bacteria colony m minutes after the initial measurement, where Q is a constant greater than 1. The predicted population increases by p% every 120 seconds. What is the value of p in terms of Q?
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指数增长・衰减与复利进阶
The function \( f\left(x\right)=236\left(1.022\right)^x \) models the value, in dollars, of a certain bank account from 1958 through 1973, where x is the number of years after the end of 1958. Which of the following is the best interpretation of “\( f\left(5\right) \) is approximately equal to 263" in this context?
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