2. Let 10000 P(t) = 900e-t + 100 describe the size of a population at time t. Find the inverse function and explain its meaning. When will the population reach size 100?

Q: 17. Lance accidentally lets a spider into the IUPUI experimental nuclear reactor. If the spider…

A: Given function, W(t)=0.01e4.5t Where W(t) is the weight of the spider(in kilograms) after t days.

Q: 5. Which of the following functions grows the slowest as x goes to infinity? O 0.01x³ O 0.001x³…

A: We can solve this as follows:

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A:

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A: The solution of given problem is followed by

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A:

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A: Topic:- calculus

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A: Solution: we know that The equation of an exponential decay function is given by where a = initial…

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A:

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A: Given:- The half-life of uranium-135 is 60 years. Suppose we have a 20 gram sample. To find:- 1.…

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A:

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A:

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A:

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A: Consider the given functions fx=1og2x,gx=xx,gx=x2,k=2x.

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A: Solution

Q: 2. Consider a population of bacteria that grows according to the function f(t)=500e^0.05t , where t…

A:

Q: Suppose that P = f(t) is the population (in millions) of the country t years after the year 2000.…

A: Given that P= f(t) is the population (in millions) of the country t years after the year 2000

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A: The function is y=abx

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A: Please refer to the image below

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A:

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A:

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A: Given, The number of gallons of a pollutant in a lake is growing according to the function…

Q: 5. Find the derivative of the following Natural Logarithm functions f(x) = In(3x – 4) a. b. 2

A:

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A: given , tank that contain 10liters of water and 50 gram of salt .  so , initial concentration =>…

Q: a) Express the new function h(x) = log2(x + 2) in terms of the original function f (X) = log2(x).…

A:

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A: y=3-2x  and  y=exat f(x)=3-2x-ex

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A: To find  The domain of (f*g) (x)

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A:

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Q: How do I answer question 30 and 31?

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A:

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A: Formula details

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A:

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A: A sample of 300g of lead-210 decays to polonium-210 according to the function given by A(t)=…

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A: We have to find the exponential function f(x)=a^x that passes through the point (3,343) and has a…

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A:

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A: The figure is:

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A:

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A:

Q: Find the exponential function f(x) = a whose graph is given. %3D f(x) =

A: Given, f(x)=ax

Q: 2) Write the derivatives of these four functions: a) 7 log8(x) b) 3ex c) 5(16x) d) 9ln(x)

A:

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A:

Q: 7. If the number of bees in a beehive are modeled by the function 6(t) = te +1 thousand bees, where…

A: The number of bees in a beehive modeled by b(t)=te-t210+1 thousand bees,where t is in months past…

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A: We know log2(mn) = log2(m) + log2(n) So we can break g(x) in the similar way,

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A: Function passes through the point (2,1/3) which satisfy the function

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A:

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.