Question

attachment below <3 pleeeaaasseeee help ! last test & please help me understand how you get the anwsers u get.

Answer 1

you have a formula given: \[P = A*e^{kt}\]

Answer 2

at t=0, the population is 3000. at = 6 you have \[3600 = 3000*e^{k*6}\]

Answer 3

so you need to solve for "k" then you will solve for \[P = 3000*e^{k*13}\]

Answer 4

to determine the population at 13 hours

Answer 5

to solve for k in \[P = A*e^{kt}\] you will need do \[e^{k*t} = P/a\] then, \[ln(e^{k*t}) = ln(P/A)\]

this becomes

\[k*t = ln(P/A)\], then solve or k --> \[k = ln(P/A)/t\]

so plug in the values, P = 3600, A = 3000, t = 6 to solve for k

Answer 6

once you have k use the forumla again to solve for P at t = 13 hours

Answer 7

:) thanks