Question

the mall odered 10,000 cookies in anticipation of children coming to visit Santa. In the first hour after opening, the cookies decreased exponentially to 9,000. Write a function expressing cookies as a function of time. Find the half-life of the cookies

Answer 1

$P(t)=P_0e^{-t/\tau}$

$For$

$t=1$ hour:

$9000=10000e^{-1/\tau}$

$\tau=-1/ln(9/10)=9.5$

$P(t)=10000e^{-t/9.5}$

For half-liffe:

$1/2=e^{-t_{1/2}/9.5}$

$t_{1/2}=-9.5ln(1/2)=6.6$ hours