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
A sample of a certain isotope takes 29 years to decay to half its original mass. The function\( s\left(t\right)=208\left(0.5\right)^{\frac{t}{29}} \) gives the approximate mass of this isotope, in grams, that remains t years after a 208-gram sample starts to decay. Which statement is the best interpretation of \( s\left(87\right)=26 \) in this context?
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指数增长・衰减与复利进阶
\( P\left(t\right)=260\left(1.03\right)^{\left(\frac{6}{4}\right)t} \)
The function P models the population, in thousands, of a certain city t years after 2001. According to the model, the population is predicted to increase by n % every 8 months. What is the value of n?
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指数增长・衰减与复利进阶
\( P\left(t\right)=230\left(1.03\right)^{\frac{3}{2}t} \)
The function P models the population, in thousands, of a certain city t years after 2001. According to the model, the population is predicted to increase by n% every 8 months. What is the value of n?
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指数增长・衰减与复利挑战
For a function \( f \), the value of \( f\left(x\right) \)is multiplied by 8 for every increase of 1 in the value of x . When x = 0, \( f\left(x\right)=5 \).Which of the following equations defines \( f \)?
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指数增长・衰减与复利挑战
For the function \( f \), for each increase in the value of x by c, where c is a posftive constant, the value of \( f\left(x\right) \) increases by a factor of 27. Which of the following equivalent forms of the function \( f \) displays \( \frac{1}{c} \) as a coefficient of x ?
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指数增长・衰减与复利挑战
A certain investment account offers a special interest rate for the first 4 months the account is open followed by a lower interest rate for the remainder of the time the account is open. Akeyla opened one of these accounts with an original account balance of $700.00 and did not make any other deposits or withdrawals. 4 months after Akeyla opened the account, the balance had increased by 0.6% of the original balance. 6 months after Akeyla opened the account, the balance had increased by an additional 0.1% of the balance at the end of the first 4 months. Every 2 months after the first 6 months, the balance had increased by an additional 0.1% of the balance 2 months before. Which of the following equations could represent the account balance \( B\left(x\right) \), in dollars, x months after the account was opened, where \( x\ge4 \)?
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指数增长・衰减与复利挑战
\( f\left(x\right)=25\left(1.40\right)^{\frac{x}{3}} \)
For the given function \( f \), the value of \( f\left(x\right) \) increases by p% for every increase of x by 6. What is the value of p?
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指数增长・衰减与复利挑战
The population of a certain city doubled every 25 years from 1660 to 1760. The population of this city was 208,000 in 1760. What was the population of this city in 1660?
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指数增长・衰减与复利进阶
\( y=7,800\left(0.85\right)^x \)
The given equation estimates the value, in dollars, of a certain car x years after it was purchased. According to the given equation, what was the estimated value, in dollars, of the car at the time it was purchased?
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指数增长・衰减与复利进阶
The function \( f\left(t\right)=30,000\left(2\right)^{\frac{t}{370}} \) gives the number of bacteria in a population t minutes after an initial observation. How much time, in minutes, does it take for the number of bacteria in the population to double?
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指数增长・衰减与复利挑战
For the function \( f \) , for every increase of 2 in the value of x, the value of \( f\left(x\right) \) increases by a factor of c, where c is a constant. Which of the following equivalent forms of function \( f \) displays the value of c as the base or the coefficient?
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指数增长・衰减与复利挑战
A model predicts that the population of a certain town was 5,000 in 2008. The model also predicts that each year for the next 5 years, the population p increased by 4% of the previous year's population. Which equation best represents this model, where x is the number of years after 2008, for \( x\le5 \)?
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