5272道题目5525 条题源记录 · 相同内容已合并
指数增长・衰减与复利挑战
\( f\left(x\right)=3,950\left(0.38\right)^{\frac{x}{12}} \)
The function \( f \) gives the value, in dollars, of a certain piece of equipment after x months of use. If the value of the equipment decreases each year by p% of its value the preceding year, what is the value of p?
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指数增长・衰减与复利挑战
The exponential function \( f \) is defined by \( f(x)=ab^x \), where a and b are positive constants. If \( f(s)=t \) and \( f(s+1)=t-0.87t \), where s and t are constants, what is the value of b?
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指数增长・衰减与复利进阶
James purchased a certain baseball card on January 1. The function \( f(x)=55(1.04)^x \), where \( 0\le x\le10 \), gives the predicted value, in dollars, of the baseball card x years after James purchased it. What is the best interpretation of the statement “\( f(7) \) is approximately equal to 72” in this context?
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指数增长・衰减与复利进阶
\( P(t)=260(1.03)^{\left(\frac{3}{2}\right)t} \)
The function P models the population, in thousands, of a certain city t years after 2009. 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
Anton is selling toys from his toy collection. When he started selling the toys, there were 2,800 toys in the collection. At the end of each week for 3 weeks after Anton started selling the toys, the number of toys in the collection had decreased by \( \frac{1}{2} \) of the toys in the collection at the end of the previous week. Which equation gives the number of toys, c, in the collection w weeks after Anton started selling the toys, where \( 0≤w<3 \) ?
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指数增长・衰减与复利进阶
The number of bacteria in a growth medium is expected to increase by 150% every 2 hours during a period of observation. The number of bacteria in the growth medium was estimated to be 7,000 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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指数增长・衰减与复利进阶
A savings account is opened with an initial deposit of $7,000. The amount of money in the account t years after the initial deposit is given by the function \( f\left(t\right)=7,000\left(1.01\right)^{2t} \). Which of the following is the best interpretation of the statement "f(3) is approximately equal to 7,430.64" in this context?
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指数增长・衰减与复利挑战
\( f\left(x\right)=3,600\left(0.28\right)^{\frac{x}{12}} \)
The function f gives the value, in dollars, of a certain piece of equipment after x months of use. If the value of the equipment decreases each year by p% of its value
the preceding year, what is the value of p?
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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 27% every 14.07 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 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. Bennett opened one of these accounts with an original account balance of $900 and did not make any other deposits or withdrawals. 4 months after Bennett opened the account, the balance had increased by 0.6% of the original balance. 6 months after Bennett 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 \( B(x) \), 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
The population of a certain city doubled every 75 years from 1663 to 1963. The population of this city was 240,000 in 1963. What was the population of this city in 1663?
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指数增长・衰减与复利进阶
A computer program models the total mass of the population of a certain type of algae after the algae was placed in an environment where it has no natural predators. According to the model, the estimated total mass of this population of algae at the end of every 6-hour period is 129% greater than the estimated total mass of this population of algae at the end of the previous 6-hour period, and the estimated total mass of this population of algae is 613.90 grams after 18 hours. Which equation best represents this model, where A is the estimated total mass, in grams, of the population of algae after x hours, and \( x<50 \)?
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