d(p) = 500e^-0.1p

Q: (1/6k^2)=(1/3k^2)-(1/k) Solve for K

A:

Q: P(t)= 952e^(0.12)t Solve for t when P=20,000

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Q: x=(2x+35)^1/2

A:

Q: solve for t:   (1+(0.03/12))^t = 5

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Q: f(0)   =170/1+6e^-2x

A:

Q: Twelve pounds of the element plutonium is released in a nuclear accident. The amount of plutonium P…

A:

Q: Solve for x using sci notation (2x)(2x) / (0.2) = 1.4 x 10^-5

A: In scientific notation, numbers like 0.0000053 will be written as 5.3x10-6

Q: solve for A, 1.35=[((1+A)^6-1)/A]

A:

Q: On a college campus of 5000 students, the spread of flu virus through the student is modeled by P(t)…

A: The spread of the flu among the students is given by the equation P(t)=50001+4999e-0.8t where, P(t)…

Q: = 1/2gt^2 for g

A: Here we have to solve D=12gt2 for g.

Q: N(t)= 250,000(.494)^t When will 10 percent of the original amount of aluminum be in use? In years

A: The given equation is: Nt=250,0000.494t To find: When will 10 percent of the original amount of…

Q: Find the slope of f (x) = ln⁡(3x^2+8)/(-2)  at (2,−1.50).

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Q: (1+1/x)^x = y. Solve for x.

A: Given: 1+1xx=y

Q: N(t)=220/5+15e^-0.7t How many people have heard after 3 days?

A: Given: Nt=2205+15e-0.7t

Q: find the exact solution 40=3(1.15)^t

A: Given query is to find the value of t.

Q: Infusion: An IV line provides a continuous flow of a drug directly into the bloodstream. Assuming A…

A: From question 4, we have m(t)=400e-0.462t. Here, the amount of drug after t hours is m(t)=Ak1-e-kt.…

Q: P(t)=700e^0.03t When will the insect population reach 1120 insects? When will the population double?

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Q: f(x)= 3•1/2^-x  -8

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Q: Solve for x  (x-3)^3/5=8

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Q: P(t)=1000e^2.0794t. How many bacteria will there be in 1.5 hours?

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Q: dv/dx - v = 3e^x

A: This is the first order linear differential equation

Continuous Probability Distributions

Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could count from 0 to a trillion seconds, billion seconds, so on indefinitely. A discrete probability distribution consists of only a countable set of possible values.

Normal Distribution

Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!