Question

The number of bacteria in a culture is given by n(t) = 400e^0.24t (t hours).
a) find t when the population is 2730.
b) Find t when the population is 4400.
b) sketch the model n(t)=400e^0.24t using all the information above.

how to do this?

Answer 1

substitute n(t) = 2730 and n(t) =4400 to find t for those two values.

Answer 2

400e^0.24t = 2730
0.24t = log2730 to the base 400e
0.24t = 1.13
t = 4.71 hours or 4 hrs 42 mins and 55 seconds

Answer 3

you remember how we talked about logarithms?
well natural log is represented as log to the base e, called ln
so ln e^0.24t = 0.24t

Answer 4

for b) it is 0.24t = log 4400 to the base 400e
0.24t = 1.2
t = 5 hours

Answer 5

@ dhatraditya Yup, I remember about it.. but, in here I got different result in doing it..
@ ishan_meswani so the t is 4.71 hrs?

Answer 6

yes

Answer 7

for the first part

Answer 8

natural log is log to the base e. e is euler's number
e is roughly 2.71

Answer 9

you must have taken log, which we ssume to be log to the base 10. what you need to do is take ln.

Answer 10

to plot the graph plot t as the x co ordinate and the population as the y axis

Answer 11

hm.. ok. thanks!

Answer 12

for the b part, somehow I got the result as 9.99.