How many bacteria will there be at​ midnight?

Question

During a research​ experiment, it was found that the number of bacteria in a culture grew at a rate proportional to its size. At

99​:00

AM there were

4 comma 0004,000

bacteria present in the culture. At​ noon, the number of bacteria grew to

4 comma 8004,800.

How many bacteria will there be at​ midnight?

Answer 1

9am 4,000 time t=0

noon 4,800 time t=3

midnight ? time t=15

4800=4000e^rt

48/40 = e^3r

3r = ln1.2

r = (ln1.2)/3

at midnight t=15

A= 4000e^(15/3(ln1.2))

A= 4000e^5ln1.2

= 9953.28