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指数增长・衰减与复利挑战
The equation \(N(m)=65(Q)^{\frac{m}{4}}\) 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
\( f\left(x\right)=1,300\left(0.5\right)^{\frac{x}{14}} \)
The function f models the intensity of a beam, f (x), in number of photons in the beam, x millimeters below the surface of a certain material. According to the model, what is the number of photons in the beam when it is at the surface of the material?
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指数增长・衰减与复利进阶
\( f\left(x\right)=3,000\left(0.75\right)^x \)
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\( \le \) 8. Which of the following is the best interpretation of 3,000 in this context?
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指数增长・衰减与复利进阶
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 6.29 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
At the start of an experiment, the pressure inside a container was 18 pounds per square inch (psi). The pressure inside the container doubled every 29 minutes after the start of the experiment. Which equation represents this situation, where y is the pressure, in psi, inside the container x minutes after the start of the experiment?
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指数增长・衰减与复利进阶
The function f is defined by \( f\left(x\right)=44\left(0.21\right)^x \) . For any positive integer n, the value of f (n) is p% less than the value of f (n- 1). What is the value of p?
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指数增长・衰减与复利进阶
The function \( f\left(x\right)=240,000\left(1.22\right)^x \) 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 (5) is approximately equal to 648,650" in this context?
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指数增长・衰减与复利挑战
At the time of posting a video, a social media channel had 67 subscribers. Each day for five days after the video was posted, the number of subscribers doubled from the number the previous day. Which equation gives the total number of subscribers, n, to the channel d days after the video was posted?
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指数增长・衰减与复利进阶
The function \( f(m)=125(5)^{\frac{m}{30}} \) represents the population of elephants m months after the initial observation. How many months since the initial observation does it take for the population of elephants to be 625 ?
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指数增长・衰减与复利进阶
By the end of March, the water level at the reservoir was 250 meters. It was projected that each month for the next 6 months, the water level, w, will decrease by 25% from the previous month. Which equation best represents this scenario, where m is the number of months after March, for m ≤ 6 ?
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指数增长・衰减与复利进阶
Liam has $150 in an account. Each year he expects to have 2.8% more money in the account than he had the previous year Which of the following models best describes how Liam expects the money in his account to change over time?
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指数增长・衰减与复利进阶
f(x) = k(1.84)x
The function f is defined by the given equation, where k is a constant. The value of f(x) increases by p% for every increase of x by 1. For which of the following functions, where k is a constant, does the value of g(x ) increase by p% for every increase of x by 4?
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