The size P of a small herbivore population at time t (in years) obeys the function  P(t)e^0.28t if they have enough food and the predator population stays constant. After how many years will the population reach 4000?

Initially, 10 grams of a radioactive substance were found in a sample. It was observed that 20% of the initial amount of radioactive substance disintegrated after 2 hours (that is, 8 grams remain after 2 hours). Find the half-life of the radioactive substance (that is, the time it takes for one- half of the initial amount to disintegrate) if the rate of disintegration of the radioactive substance is In z 1 2 0.7 proportional to the amount of the substance present at time t. You must begin your solution process by 3 considering the proportional relationship presented below. Use the natural logarithm table to the right 1.1 to provide an approximate answer. Your work must support your answer. 4 1.4 1.6 dA a A 6 1.8 dt 1.9 2.1 9 2.2 10 2.3 7,

The height of a tree after t years is h(t) = 30 – %3D 1 1 25 feet when t> 1. How fast is the tree growing t after 5 years?

The total expenditures (in millions) of current dollars for pollution abatement and control during the poriod from 2000 through 2019 can be approximatod by the function P(x) = 175.17 e008x, where x0 corresponds to the year 2000. (a) In what year would the total expenditures reach $209 million dollars? (b) If this model remains accurate, when would the total expenditures reach $481 million?

A material has an initial of 15 units. Which equation models the amount of the material y, decaying exponentially at a rate of 23% over time x

The population of a town grows at a rate proportional to the population at time t. The initial population of 250 increases 20% in 9 years. What will the population be after 15 years? How fast is the population growing at t= 15?

Suppose a species of fish in a particular lake has a population that is modeled bythe logistic population model with growth rate k, carrying capacity N, and time tmeasured in years. Adjust the model to account for each of the following situations. * One hundred fish are harvested each year.* One-third of the fish population is harvested annually.* The number of fish harvested each year is proportional to the square root of thenumber of fish in the lake. I was hoping to compare my answer to yours because I am a little confused if I did it right. Thank you for your time and effort.

Newton's Law of Cooling states that the temperature of a heated object decreases exponentially over time toward the temperature of the surrounding medium. Suppose that a pizza is removed from a 600°F oven and placed in a room whose temperature is 60°F. The temperature u (in °F) of the pizza at time t (in minutes) can be modeled by u(t)=60+540g-0.073t (a) According to the model, when will the temperature of the pizza be 500°F? (b) According to the model, when will the temperature of the pizza be 310°F? (a) t= minutes (Do not round until the final answer. Then round to the nearest minute as needed.) w an example Textbook Clear all

Find the population of fish at 10 years if p(0) = 1000

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