The number of bacteria in a culture is modeled by the functi

The number of bacteria in a culture is modeled by the function n(t) =30^rt, where t is in hours. If there are 90 bacteria after 7 hours, determine the value of r, leave your answer in exact form. Using r, complete the model n(t) = Use the model to determine how many hours it will take for the number of bacteria to reach 270. Simplify your answer completely. Be sure to label the units.

Solution

Function n(t) = 30^(rt)

90 = 30^(7r)

Taking log both side

log 90 = 7r*log(30)

log(90)/log(30) = 7r

r = (3/7)

(b) n(t) = 30^(rt)

270 = 30^(rt)

taking log both side

log (270) = rt log (30)

rt = log(270)/log(30)

t = 9*(7/3)

t = 21

Answer