Leland got stung by a bee at a picnic. He took a 50 milligram dose of medicine to help relieve the swelling and itching. The medicine has a half-life of 8 hours. He was very sleepy the rest of the day and wondered how long the medicine would stay in his system. Hint: A basic half-life equation would be in the form: M (t) = A(0.5)7 Where M(t)= final amount, A-initial amount, t= time, and h= half-life 1. Write a function that models the amount of medicine in Leland's system based on the number of hours that have passed: 2. Approximately what amount of medicine will remain in Leland's system when 20 hours have passed. (Show your equation)

Q: Kia invests $2500 at 4% compounded continuously.  Using the formula A(t) = Pert , find what time…

A:

Q: if the principal p is invested at an interest rate r compounded annually, the amount after t years…

A: Here, A=20,000P=10,000r=15%=0.15

Q: Find the half-life of radioactive substance Plutonium-241; A(t) = A0e-0.053t

A: To get the initial mass of the substance, put t=0. A(0)=A0 e-0.053 0=A0 e0=A0 The half-life of the…

Q: The doubling period of a bacterial population is 10 minutes. At time t = 80 minutes, the bacterial…

A: Doubling time = 10 minutes at t = 80 minutes, P  = 70000

Q: The initial population of pigs in a farm is 125. Given that the growth rate per year is 7.5%,…

A: Given that The initial population of pigs in a farm is 125. P0 = 125 the growth rate per year r =…

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.