Apopulation 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.

(a) .

(b) 1020

Step-by-step explanation:

The continuous exponential growth model is defined as

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

Base is e because the population growth is continuous.

Therefore, the required model is  .

(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.

Therefore, the bacterial population after 36 hours is 1020.

step-by-step explanation:

p = 6s

step-by-step explanation: