Question
his Question. 1 p .1%) 16 of30 (28 complete) A chemical substance has a decay rate of 7 4% per day The rate of change of an amount N of the chemical is given by the equation IN ???? -0074 N where t is the number of days since decay began Complete parts a) through c) a) Let No represent the amount of the chemical substance att-0 Find the exponential furnction that models the situation b) Suppose that 400 g of the chemical substance is present at 1-0 How much will remain after 2 days? After 2 days.g will remain Round to the nearest whole number as needed) c) After how many After days, half of the chemical substance wil emain. days wil half of the 400 g of the chemical substance remain? Round to one decimal place as needed ) Eriter your ansewer i each or inme answer boxes
Explanation / Answer
dN/dt= -0.074N
dN/N=-0.074dt
Integrating
ln N= -0.074t +C
N(t)= C e-0.074t
at t=0,N(t)=N0
So we will get
N(t)= N0e-0.074t
b.N(2) = 400 e-0.074(2)= 345 g
c. 200 = 400 e-0.074t
1/2 = e-0.074t
ln 0.5=-0.074t
t= 9.4 days
