Applications of Derivative (Exponential Growth and Decay)

MUFY MATHEMATICS UNIT 1 - STUDY AREA 3 9. After t years the value, V, in dollars of a car purchased for $30 000 when new is given by P = P,e-0.0251 (a) Find the rate in dollars per year at which the car is depreciating after 10 years? (b ) After how many years will the car be worth half its value when new? 10. The concentration of a drug in a patient's bloodstream t hours after it is administered can be approximately modeled by C = 0.3e-12. From the model, (a) What is the concentration of the drug two hours after it is administered? ( b ) at what rate is the drug concentration decreasing after 2 hours? 11. Food prepared for 'take-away' is susceptible to contamination from bacteria. To kill the bacteria prior to serve the food and to ensure that it is fir for human consumption, the food is subjected to a temperature of 130 C for a period of time. The number of live bacteria in a hamburger after t minutes at a temperature of 130 C can be approximated by B = 2000e-", where t 2 0. Using this model, (a) find the initial number of bacteria present in the hamburger. ( b ) estimate the time taken, correct to the nearest tenth of a minute, to kill 50% of the bacteria. (c) estimate the percentage of bacteria, correct to one decimal place, that will still be alive after 10 minutes. (d) estimate the average rate of decrease in the number of live bacteria over the first ten minutes. (e) sketch the graph of the function B = 2000e-0.2t (f ) estimate the rate of decrease of the number of bacteria when half of the bacteria have been killed