A population of bighorn sheep: A certain group of bighorn sheep live in an area where food is plentiful and conditions are generally favorable to bighorn sheep. Consequently, the population is...

A population of bighorn sheep: A certain group of bighorn sheep live in an area where food is plentiful and conditions are generally favorable to bighorn sheep. Consequently, the population is thriving. There are initially 30 sheep in this group. Let N = N (t) be the population t years later. The population changes each year because of births and deaths. The rate of change in the population is proportional to the number of sheep currently in the population. For this particular group of sheep, the constant of proportionality is 0.04.

a. Express the sentence “The rate of change in the population is proportional to the number of sheep currently in the population” as an equation of change. (Incorporate in your answer the fact that the constant of proportionality is 0.04.)

b. Find a formula for N.

c. How long will it take this group of sheep to grow to a level of 50 individuals?