Question

use the formula P=Ie^kt. a bacterial culture has an initial population of 10000 . If its population declines to 3000 in 8 hours , what will it be at the end of 10 hours ?

Answer 1

P(0)=10000, substitute this info into the equation P=Ie^kt,
10000=Ie^0 implies 10000=I,

updating the equation, P(t)=10000e^kt
P(8)=3000, substitute this into the equation above,
3000=10000e^8k,
0.3=e^8k,
put natural logarithm at both right hand side and left hand side of this equation,
ln 0.3 = 8k,
1/8 ln 0.3 = k
-0.1505=k

now we have P(t)=10000e^(-0.1505t).

just plug in t=10 into the equation and you'll get the answer :)