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?

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

updating the equation, P (t) = 10000e^ktP (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