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Problem 1. (10 pts) The half life of a substance is 5 years. There are 30...
Radioactive substance decays so that after t years, the amount remaining, expressed as a percent of the original amount, is A(t)=100(1.6)^(-t)
Radioactive substance decays so that after t years, the amount remaining, expressed as a percent of the original amount, is A(t)=100(1.6)^(-t). a) Determine the function A’, which represent the rate of decay of the substance. b) what is the half-life for this substance? c) what is the rate of decay when half the substance has decayed?
Element X is a radioactive isotope such that every 30 years, its mass decreases by half....
Element X is a radioactive isotope such that every 30 years, its mass decreases by half. Given that the initial mass of a sample of Element X is 4000 grams, write a function showing the mass of the sample remaining after t years, where the annual decay rate can be found from a constant in the function. Round all coefficients in the function to four decimal places. Also, determine the percentage rate of decay per year, to the nearest hundredth...
A scientist begins with 250 grams of a radioactive substance. After 250 minutes, the sample has...
A scientist begins with 250 grams of a radioactive substance. After 250 minutes, the sample has decayed to 36 grams. Write an exponential equation f(t) representing this situation. (Let f be the amount of radioactive substance in grams and t be the time in minutes.) f(t) 250e 0.0087t x To the nearest minute, what is the half-life of this substance? 89 min Use the model for continuous exponential decay, y = Ao e-kt, where y is the amount of radioactive...
h= half life a0 = original amount a(t) = amount present after t years t =...
h= half life
a0 = original amount
a(t) = amount present after t years
t = time
What information do you need?
TH 100 - D100 Use equation : acca un Page 4 of 5 4. Suppose we have Xo amount of a certain radioactive substance. It has been observed that this substance losses 5% of its mass every 10 years. @ How much of the initial mass Xo remains after 10 years? What about 20 years? (b) Use the...
Please answer the following questions using exponential and logarithmic models. 4) A wooden artif...
Please answer the following questions using exponential and logarithmic models. 4) A wooden artifact from an archaeological dig contains 70 percent of the Carbon-14 that is present in living trees. To the nearest year, about how many years old is the artifact? (The half-life of Carbon-14 is 5730 years.) In years 5) A tumor is injected with 0.5 grams of Iodine-125, which has a decay rate of 1.15% per day. Write an exponential model representing the amount of Iodine-125 remaining...
A radioactive substance decays at a rate proportional to the amount present at ime t (in...
A radioactive substance decays at a rate proportional to the amount present at ime t (in hours). Initially, Ao grams of the substance was present, and after 10 hours, the mount has decreased by 20% How long will it take the substance to decay to 40? hat is the half life of this substance? Hint: the half-life is the time required for half of the initial substance to decay)
Applications of Exponential Equations Many real-life situations can be modeled by an exponential ...
ANSWER ALL PLEASE!
Applications of Exponential Equations Many real-life situations can be modeled by an exponential growth function of the form A(t) Ao ett constant that affects the rate of growth or decay, and t represents time. Using your knowledge of writing exponential equations that you did in the beginning of this chapter, what would A or an exponential decay function of the form A(t)-A ett where k represents the represent? 1. The amount of carbon-14 present in animal bones...
Review Constants Periodic a substance active times that the countable and will therefore decay by my...
Review Constants Periodic a substance active times that the countable and will therefore decay by my name of processes the decay Del decay of the day of radioactive comm o der Therefore theme of daycan t orbed by the megrated w omen e n we used to describe the food chemical con In where the mo s t coloraty t he com by man of these quo ng 0. the world when contre long for fraction remaining - - (0.5)"...
Modeling Exponential Growth and Decay A scientist begins with 240 grams of a radioactive substance. After...
Modeling Exponential Growth and Decay A scientist begins with 240 grams of a radioactive substance. After 250 minutes, the sample has decayed to 34 grams. a. Rounding to four decimal places, write an exponential equation, R(t) = Aekt, representing this situation, using the variablet for minutes. R(O) = b. To the nearest minute, what is the half-life of this substance? The half-life is approximately minutes.
please show answer before and after rounding Finding the rate or time in a word problem...
please show answer before and after rounding
Finding the rate or time in a word problem on continuous... The mass of a radioactive substance follows a continuous exponential decay model, with a decay rate parameter of 9.1% per day. Find the half-life of this substance (that is, the time it takes for one-half the original amount in a given sample of this substance to decay). Note: This is a continuous exponential decay model. Do not round any intermediate computations, and...
Element X is a radioactive isotope such that every 30 years, its mass decreases by half. Given that the initial mass of a sample of Element X is 4000 grams, write a function showing the mass of the sample remaining after t years, where the annual decay rate can be found from a constant in the function. Round all coefficients in the function to four decimal places. Also, determine the percentage rate of decay per year, to the nearest hundredth...
A scientist begins with 250 grams of a radioactive substance. After 250 minutes, the sample has decayed to 36 grams. Write an exponential equation f(t) representing this situation. (Let f be the amount of radioactive substance in grams and t be the time in minutes.) f(t) 250e 0.0087t x To the nearest minute, what is the half-life of this substance? 89 min Use the model for continuous exponential decay, y = Ao e-kt, where y is the amount of radioactive...
h= half life
a0 = original amount
a(t) = amount present after t years
t = time
What information do you need?
TH 100 - D100 Use equation : acca un Page 4 of 5 4. Suppose we have Xo amount of a certain radioactive substance. It has been observed that this substance losses 5% of its mass every 10 years. @ How much of the initial mass Xo remains after 10 years? What about 20 years? (b) Use the...
A radioactive substance decays at a rate proportional to the amount present at ime t (in hours). Initially, Ao grams of the substance was present, and after 10 hours, the mount has decreased by 20% How long will it take the substance to decay to 40? hat is the half life of this substance? Hint: the half-life is the time required for half of the initial substance to decay)
ANSWER ALL PLEASE!
Applications of Exponential Equations Many real-life situations can be modeled by an exponential growth function of the form A(t) Ao ett constant that affects the rate of growth or decay, and t represents time. Using your knowledge of writing exponential equations that you did in the beginning of this chapter, what would A or an exponential decay function of the form A(t)-A ett where k represents the represent? 1. The amount of carbon-14 present in animal bones...
Review Constants Periodic a substance active times that the countable and will therefore decay by my name of processes the decay Del decay of the day of radioactive comm o der Therefore theme of daycan t orbed by the megrated w omen e n we used to describe the food chemical con In where the mo s t coloraty t he com by man of these quo ng 0. the world when contre long for fraction remaining - - (0.5)"...
Modeling Exponential Growth and Decay A scientist begins with 240 grams of a radioactive substance. After 250 minutes, the sample has decayed to 34 grams. a. Rounding to four decimal places, write an exponential equation, R(t) = Aekt, representing this situation, using the variablet for minutes. R(O) = b. To the nearest minute, what is the half-life of this substance? The half-life is approximately minutes.
please show answer before and after rounding
Finding the rate or time in a word problem on continuous... The mass of a radioactive substance follows a continuous exponential decay model, with a decay rate parameter of 9.1% per day. Find the half-life of this substance (that is, the time it takes for one-half the original amount in a given sample of this substance to decay). Note: This is a continuous exponential decay model. Do not round any intermediate computations, and...
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