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
\( C\left(t\right)=240\left(\frac{53}{52}\right)^{t-15}+7 \)
The function C gives the estimated number of cephalopods, a class of marine animal, in a certain area, where t is the number of months since a study began. How many months after the study began was the number of cephalopods in the area estimated to be 247?
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指数增长・衰减与复利进阶
The current value of a house is $174,000, and this value increases by 2.4% each year from the value of the previous year. Which function \( f \) gives the value, in dollars, of the house x years from now?
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指数增长・衰减与复利挑战
The number of bacteria in a liquid medium doubles every hour. There are 66,000 bacteria in the liquid medium at the start of an observation. Which of the following represents the number of bacteria, y, in the liquid medium t hours after the start of the observation?
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指数增长・衰减与复利挑战
The function \( f\left(n\right)=7\left(20.44\right)^{\frac{n}{4}} \) 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・衰减与复利挑战
Each year, the value of an investment increases by 0.69% of its value the previous year. Which of the following functions best models how the value of the investment changes over time?
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指数增长・衰减与复利挑战
In a certain state, the population of pheasants, a type of bird, is estimated each year by counting the number of pheasants observed along certain roads in the state. On average, each year from 2005 to 2015 the number of pheasants counted per mile of road decreased by 3.5% of the number of pheasants per mile of road the previous year. Based on this average, if there were 6.22 pheasants per mile of road in this state in 2005, which of the following best approximates the number of pheasants per mile of road in 2015?
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指数增长・衰减与复利挑战
\( f\left(x\right)=2,000\left(1.005\right)^{3x} \)
The given function \( f \) models the balance of a bank account, in dollars, x years after it is opened. Which statement is the best interpretation of \( \left(1.005\right)^{3x} \)?
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指数增长・衰减与复利进阶
\( y=500\left(2\right)^{2x} \)
The equation gives the estimated number of online newsletter subscribers at the end of every six-month period, x, starting from the end of January 1997, where \( 0\le x\le4 \). Which statement is the best interpretation of the y-intercept of the graph of this equation in the xy-plane?
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指数增长・衰减与复利进阶
The relationship between the variables x and y is defined by an exponential equation. When \( x=0 \) , the value of y is 90, and for every increase in the value of x by 1, the corresponding value of y increases by 20% of its previous value. Which equation represents this relationship?
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指数增长・衰减与复利挑战
\( z\left(w\right)=\left(0.829\right)^{2w} \)
The function z is defined by the equation shown. The value of \( z\left(w\right) \) decreases by p% for each increase by 1 in the value of w. Which of the following is closest to the value of p?
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指数增长・衰减与复利挑战
\( f\left(x\right)=66\left(b\right)^x \)
In the given function, b is a positive constant. For every increase in the value of x by 1, the value of \( f\left(x\right) \) increases by c%, where \( 0<c<100 \). Which expression gives the value of c in terms of b?
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指数增长・衰减与复利挑战
The population of a certain city doubled every 75 years from 1652 to 1952. The population of this city was 160,000 in 1952. What was the population of this city in 1652?
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