Answer: a) N(t) = 950e^0.0475t b) 1020
Step-by-step explanation:
a)
N(t) = 950e^0.0475t.
N/B — Base is e (exponential) because growth is continuous.
b)
N = {36/24} =(approximately) 1020
Answer:
(a) [tex]N(t)=950e^{0.0475t}[/tex].
(b) 1020
Step-by-step explanation:
The continuous exponential growth model is defined as
[tex]y=ae^{kt}[/tex]
where, a is initial value, k is growth rate and t is time.
(a)
Initial population: a = 950
Continuous growth rate : k = 4.75% = 0.0475
So, the exponential function, N(t), that represents the bacterial population after t days is
[tex]N(t)=950e^{0.0475t}[/tex]
Base is e because the population growth is continuous.
Therefore, the required model is [tex]N(t)=950e^{0.0475t}[/tex] .
(b)
We need to find the bacterial population after 36 hours, to the nearest bacterium.
24 hours = 1 day
36 hours = 36/24 = 1.5 day
Substitute t=1.5 in the above equation.
[tex]y=950e^{0.0475(1.5)}[/tex]
[tex]y=1020.15717199[/tex]
[tex]y=1020[/tex]
Therefore, the bacterial population after 36 hours is 1020.
