Question

A population of 950 bacteria grows continuously at a rate of 4.75% per day. (a) Write an exponential function, N(t), that represents the bacterial population after t days and explain the reason for your choice of base. (b) Determine the bacterial population after 36 hours, to the nearest bacterium.

Answer 1

Answer:

(a) $N(t)=950e^{0.0475t}$.

(b) 1020

Step-by-step explanation:

The continuous exponential growth model is defined as

$y=ae^{kt}$  

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

$N(t)=950e^{0.0475t}$  

Base is e because the population growth is continuous.

Therefore, the required model is $N(t)=950e^{0.0475t}$  .

(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.

$y=950e^{0.0475(1.5)}$  

$y=1020.15717199$  

$y=1020$  

Therefore, the bacterial population after 36 hours is 1020.

Answer 2

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