Exponential Functions Word Problems

A bacteria culuture started with 8500 bacteria. In two hours, the number of bacteria had reached 9775. Find an expression for the number of bacteria t hours after it was first observed. Using your answer to (a), find the number of bacteria after 10 hours. When will the number of bacteria reach 4000?
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two rats, one male one female,
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Two rats were brought to an Island, where there are no any natural predators. The original female gives birth to 3 male and 3 female rats on January 1 and produces another liter (3 male & 3 female) every 40 days thereafter. Each born female will produce her first litter after 120 days of her birth and will continue producing every 40 days. Come up with general formula for the number of rats in one year.
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The rat population in a major metropolitan city is given by the formula n(t)= 73 e^{0.015 t} where t is measured in years since 1990 and n(t) is measured in millions. What was the rat population in 1990 ? What is the rat population going to be in the year 2005 ?
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In 1999, the world`s population reached 6 billion and was increasing at a rate of 1.3% per year. Assume that this growth rate remains constant. Write a formula for the world population (in billions) as a function of the number of years since 1999.
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The population of a certain city was 199000 in 1998, and the observed relative growth rate is 6 percent per year. (a) Find a function that models the population after t years
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The air in a factory is being filtered so that the quantity of a pollutant, P, is decreasing according to the function P=Poa^t, where t is time in hours. If 10% of the pollution is removed in the first 5 hours, what percentage is left after 10 hours?
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The afrrican bush elephant is the largest land animal and weighs eight tons. Write the amount in exponential form
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The world population in 1950 was estimated to be 2.5 bilion. The population has grown exponentially so that in 2008 there were an estimated 6.8 billion. Determine the yearly growth factor.
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A ball is dropped out of a window of a tall building. If it hits the ground 3.5 seconds later, how high above ground is the window?
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The afrrican bush elephant is the largest land animal and weighs eight tons. Write the amount in exponetual form
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crabon14 decays at a rate of 11.4%every 1000 years. a. write a formula for the quantity,Q, with an initial 200gram sample as a function of time t, in years b. How much of the 200 grams will remain after 1500 years
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In 8 days, a sample of Vanadium48 decays to 1/ squareroot of 2 of its original amount. Determine the halflife of Vanadium48.
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A certain radioactive substance decays half of itself everyday. Initially, there are 10 grams. How much substance will be left after 8 days?
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2. Examine the rise in gasoline prices from 1997 to 2006. The price of regular unleaded gasoline in January 1997 was $1.26 and in January 2006 the price of regular unleaded gasoline was $2.31 (Bureau of Labor Statistics, 2006). Use the coordinates (1997, 1.26) and (2006, 2.31) to find the slope (or rate of change) between the two points.
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Write an exponential function to model the situation. Then predict the value of the function after 5 years. A population of 450 animals that decreases at an annual rate of 19%.
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After the mill closed, Steeltown PA started losing people exponentially. If Steeltown`s population was 100,000 in 1970, and 59,874 people in 1980, model the population with an exponential function.
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the period of a simple pendulum varies directly as the square root of its length. If a pendulum three feet long has a period of 4.8 seconds, find the period of a pendulum half as long.
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graph the function, not by plotting points, but by starting from the graphs in figures 2 and 5. state the domain , range ,and asymptote. g(x)=2^x3
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The rat population in a major metropolitan city is given by the formula where is measured in years since 1990 and is measured in millions.
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Suppose the Population of D.C. in January of 2006 was 580,000 and 2 percent of them moved every 6 months. How many people would be left on January 2009?

A biologist is researching a newlydiscovered species of bacteria. At time t = 0 hours, he puts one hundred bacteria into what he has determined to be a favorable growth medium. Six hours later, he measures 450 bacteria. Assuming exponential growth, what is the growth constant "k" for the bacteria? (Round k to two decimal places.)

If you put 25 cents in a bank and your money doubles each year, how long will it take to have a billion dollars?

wendy, a loan officer at a bak has $1000000 to lend and is required to obtain an average return of 18% per year. if she can lend at the rate of 19% or at the rate of 16%, how much can she lend at the 16% rate and till meet her requirmeents?

A baby weighing 7 pounds at birth may increase in weight by 11% per month. How much will the baby weigh after 1 year?

A vendor can sell 300 trees for $15 each. The trees cost the vendor $5 each to cut and deliver to sell. If the trees are sold at a higher price, then for each $1 increase in price, 12 fewer trees will be sold

Sapose the number of cars, c, on first ave. in a city over a perould of time t, in months is greater on a rectangular cordnent system where time is on the horazonal axis. sapose the number of cars on first ave. can be modified by an exponential function C=p(a)^t where p is the munber of cars on the road on the first day recorded. If you commuted to work each day along first ave. would you prefer that the value of "a" be between 0,1 or larger than 1?

the half life of radioactive cesium 137 is 30.2 years. If we have 750 poiunds of radioactive cesium, how much will be lost over the next 500 years?

If there are 45 rats in a New York deli and the number of rats doubles every 7 days how long will it take for the deli to have 100,000 rats?

anna needed to let everyone in the music club know the time of its next meeting. she called two people and asked each of them to call two other people, and so on. if each phone call takes one minute, how many phone calls were made during the fifth minute?

An air freshener starts with 31 grams and evaporates. In each of the following cases, write a formula for the quantity, Q grams, of air freshener remaining t days after the start