Answer to Question #100434 in Algebra for Naomi Kiel

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