precalculus math

Question

1. The most common use of radioactive isotopes in medicine is to diagnose disease. Typically, radioactive materials are injected into the body and then radiation-detecting cameras are used to build images of affected body parts or particular types of cells.The equation shown models the amount of a radioactive isotope y(t) in the bloodstream t minutes after it is injected.y yoe-0.005a. Does this model represent a situation of exponential growth or decay? Explain how you know.b. What is the rate of growth or decay? c. what do you think the constant yo represent in this model?d. The isotope is no longer useful in diagnostic tests when 95% of the sample has decayed. Determine how long a sample will be useful in a diagnostic lab. Be sure to show how you determined your solution.e. One student suggested a better representation of this function model would be y =-. Explain why you agree or disagree with this student

Answer 1

This is exponential decay since your growth factor (-.005) is negative

yo is the initial amount (this would be at t=0)

when 95 % of the material has decayed only 5% remains

so your equation is .05= e^.005t To solve for t start by taking the natural log of both sides

ln.05 = lne^.005t

ln .05 = .005t

t= (ln.05)/.005

t=599