(a)
To calculate: The exponential model for the concentration D after t hours of injection in the bloodstream of a patient in milligrams per milliliter if soon after injection it is
(b)
To calculate: The concentration D after
(c)
To graph: The function of concentration D after t hours of injection in the bloodstream of a patient in milligrams per milliliter obtained in part (a) if soon after injection it is
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Chapter 4 Solutions
CALCULUS APPLIED APPROACH >PRINT UGRADE<
- A driver of a car stopped at a gas station to fill up his gas tank. He looked at his watch, and the time read exactly 3:40 p.m. At this time, he started pumping gas into the tank. At exactly 3:44, the tank was full and he noticed that he had pumped 10.7 gallons. What is the average rate of flow of the gasoline into the gas tank?arrow_forwardThe half-life of radioactive actinium ( 227AC ) is 21.77 years. What percent of a present amount of radioactive actinium will remain after 19 years?arrow_forwardMaria, a biologist is observing the growth pattern of a virus. She starts with 100 of the virus that grows at a rate of 10% per hour. She will check on the virus in 24 hours. How many viruses will she find?arrow_forward
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- For the following exercises, use this scenario: A doctor prescribes 300 milligrams of a therapeutic drug that decays by about 17 each hour. Write an exponential model representing the amount of the drug remaining in the patient's system after t hours. Then use the formula to find the amount of the drug that would remain in the patient's system after 24 hours. Round to the nearest hundredth of a gram.arrow_forwardWhat is the difference between the equation for exponential growth versus the equation for exponential decay?arrow_forwardThe number of bacteria in a culture is increasing according to the law of exponential growth. After 1 hour there are 100 bacteria, and after 2 hours there are 200 bacteria. How many bacteria will there be after 3 hours?arrow_forward
- For the following exercises, use this scenario: A biologist recorded a count of 360 bacteria present in a culture after 5 minutes and 1,000 bacteria present after 20 minutes. Rounding to six significant digits, write an exponential equation representing this situation. To the nearest minute, how long did it take the population to double?arrow_forwardThe population of a lake of fish is modeled by the logistic equation P(t)=16,1201+25e0.75t, where t is time inyears. To the unrest hundredth, how manyyears will it take the lake to reach 80% of its carrying capacity?For the following exercises, use a graphing utility to create a scatter diagram of the data given in the table.Observe the shape of the scatter diagram to determine whether the data is best described by an exponential,logarithmic, or logistic model. Then use the appropriate regression feature to find an equation that models thedata. When necessary, round values to five decimal places.arrow_forwardThe population of a culture of bacteria is modeled by the logistic equation P(t)=14,2501+29e0.62t where t is inarrow_forward
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