Question

a colony of bacteria grows exponentially according to the function N(t)=100e^0.045t where N measures in grams and t is measured in days.

1. determine the initial amount of bacteria??
2. what is the population after 5 days??
3. how long will it take the population to reach 140 grams??

Answer 1

1. The initial amount would be when t=0.
N(0)=100e^0 = 100*1 = 100 grams of bacteria initially.

2. t=5
\[N(5)=100e^{.045*5}\]
N(5)=100*1.252323
N(5)=125.2323 grams of bacteria.

3. N(t)=140
140=100e^.045t
1.4=e^.045t
t is approximately 1.3384, so 1.3384 days.