After the introduction of foxes on an island, the number of rabbits on the island decreases by 4.5% per month. If y(t) equals the number of rabbits on the island t months after foxes were introduced, find the rate constant k for the exponential decay function y(t) = y0ekt.

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A: Given:- Under laboratory conditions the half-life of ozone is approximately 25 hours. If Q =Q0 ekt…

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Q: 2-The radioactive isotope of lead, Pb-209, decays at a rate proportional to the amount present at…

A: image is attached

Q: Because of the absence of predators, the number of rabbits on a small island increases at a rate of…

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A: Let's find.

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Q: 1. The population of a town grows at the rate proportional to population present at any time t. The…

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Q: A bacterial population B is known to have a growth rate proportional to B itself. If between 3pm and…

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A: Consider the given D.E. and integrate to find y(t).

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A: The relation between the half-life and decay constant is given by: t1/2=ln2k Given: t1/2=30 years

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Q: What happens to the rate of change of the exponential function y = ax as a becomes larger?

A: To explain the given problem

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A: Given that X ~ Exp(0.7).

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Q: ) An environmental study estimates that t years from now, the level of carbon monoxide in the air of…

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Q: A mathematical model for population growth over short intervals is given by P=P0ert​, where P0 is…

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Q: The decay equation for radon-222 gas is known to be y = y0 e-0.18t, with t in days. About how long…

A: The decay equation for radon-222 gas is known to be y = y0 e-0.18t, with t in days. About how long…

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Q: Suppose it is known that the population of the community in Problem 1 is 10,000 after 3 years. What…

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Q: A bacterial population B is known to have a growth rate proportional to B itself. If between 3pm and…

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Q: A 5kg sample of plutonium-239 has a half-life of 21,400 years by emitting a 5.157 MeV (million or…

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Q: (b) A company has an income stream with rate of income given by f(t) = 1 – 0.02t measured in…

A: Given: A company has an income stream with a rate of income given by f(t)=1-0.02t where f(t) is…

Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.