5272道题目5525 条题源记录 · 相同内容已合并
指数增长・衰减与复利进阶
The growth of the number of bacteria in a certain population is modeled by a function that increases exponentially over time. Which of the following could describe how the number of bacteria in the population changes each hour?
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指数增长・衰减与复利挑战
According to a model, the estimated volume of a certain Douglas fir tree increases by 14.3% for every increase of 100 centimeters in the tree's height. The equation \( y=ab^{\frac{x}{100}} \) represents this model, where y represents the estimated volume, in cubic centimeters, of this Douglas fir tree, x represents the tree's height, in centimeters, and a and b are constants. In this equation, what is the value of b?
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指数增长・衰减与复利进阶
Harper has $110 in an account. Each year she expects to have 2.7% more money in the account than she had the previous year. Which of the following models best describes how Harper expects the money in her account to change over time?
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指数增长・衰减与复利进阶
A researcher observes a sample of a nuclide. An exponential model estimates that the mass, in grams, of the sample decreases by 23% every 11.69 minutes. Which of the following equations could represent this model, where M is the estimated mass, in grams, of the sample t minutes after the researcher began observing the sample?
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指数增长・衰减与复利挑战
A researcher observes a sample of a nuclide. An exponential model estimates that the mass, in grams, of the sample decreases by 22% every 11.11 minutes. Which of the following equations could represent this model, where M is the estimated mass, in grams, of the sample t minutes after the researcher began observing the sample?
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指数增长・衰减与复利进阶
A sample of a certain isotope takes 29 years to decay to half its original mass. The function \( s\left(t\right)=136\left(0.5\right)^{\frac{t}{29}} \) gives the approximate mass of this isotope, in grams, that remains t years after a 136-gram sample starts to decay. Which statement is the best interpretation of \( s\left(58\right)=34 \) in this context?
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指数增长・衰减与复利进阶
Antonia has $130 in an account. Each year she expects to have 2.5% more money in the account than she had the previous year. Which of the following models best describes how Antonia expects the money in her account to change over time?
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指数增长・衰减与复利挑战
A model estimates that at the end of each year from 2015 to 2020, the number of rabbits in a population was 170% more than the number of rabbits in the population at the end of the previous year. The model estimates that at the end of 2016, there were 216 rabbits in the population. Which of the following equations represents this model, where n is the estimated number of rabbits in the population t years after the end of 2015 and \( t\le5 \) ?
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指数增长・衰减与复利挑战
The potential difference across a capacitor in an electric circuit is initially 16 volts and decreases with time, as shown in the graph. Which of the following is closest to the time, in seconds, from the initial measurement at which the potential difference across the capacitor is 15% of its initial value?
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指数增长・衰减与复利挑战
A sample of a certain isotope takes 29 years to decay to half its original mass. The function \( s(t)=128(0.5)^{\frac{t}{29}} \) gives the approximate mass of this isotope, in grams, that remains t years after a 128-gram sample starts to decay. Which statement is the best interpretation of \( s\left(58\right)=32 \) in this context?
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指数增长・衰减与复利挑战
The function \( f \) is defined by \( f\left(x\right)=53\left(0.15\right)^x \) . For any positive integer n, the value of \( f\left(n\right) \) is p% less than the value of \( f\left(n-1\right) \). What is the value of p?
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指数增长・衰减与复利挑战
The number of bacteria in a growth medium is expected to increase by 170% every 2 hours during a period of observation. The number of bacteria in the growth medium was estimated to be 5,000 when the period of observation began. Which function P gives the expected number of bacteria in this growth medium t hours after the period of observation began?
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