A population of protozoa develops with a constant relative growth rate of 0.6671 per member per day. On day zero the population consists of 4 members. Find the population size after 7 days. Since the relative growth rate is 0.6671, then the differential equation that models this growth is

The population size after 7 days is about 427.

Step-by-step explanation:

If is the value of a quantity at time and the if the rate of change of with respect to is proportional to its size at any time, then

where is a constant.

This equation is sometimes called the law of natural growth (if ).

The only solutions of the differential equation are the exponential functions

Let be the population size and let be the time variable, measured in hours. Since the relative growth rate is 0.6671, then the differential equation that models this growth is

According with the above information the solution to this differential equation is

On day zero the population consists of 4 members .

Therefore, the population size after 7 days is

about 427.

d

step-by-step explanation:

the monthly balance will be $75,000