A culture started with 4,000 bacteria. after 7 hours, it grew to 5,200 bacteria. Predict how many bacteria will be present after 9 hours

Start with trying to figure out rate (r):

P = i•e^rt

5200 = 4000•e^ (r•7)

5200/4000 = 1.3 = e^7r

ln 1.3 = ln (e^7r)

.262 = 7r•1, because the ln (e) = 1

r =.262/7 =.0375

Now that you have the rate, plug in that for r and 9 hours as the new t, with again our 4200 as the i

P = i•e^rt = 4200•e^ (.0375•9)

P = 4200•1.401 = 5,886 bacteria