The population of a colony of mosquitoes obeys the law of uninhibited growth.If N is the population of the colony and t is the time in days, express N as a function of t.E

Answer 1

Uninhibited Growth and Decay models:

Things that grow or decay proportionally to itself, with no limits, is known as "uninhibited" growth/decay.

Uninhibited Growth in Algebra 2

The uninhibited growth formula is A(t) = A₀e^kt, where A₀ is the initial value, k is the growth factor, and t is the amount of time. If you have something like a doubling time, but no growth factor, you can solve for the growth factor by plugging in A(t), A₀, and t, and solving for k.

Derivation from Calculus/Differential Equations

The derivation of the model from algebra 2 starts with the original equation based on the definition:

growth proportional to initial amount, with no limits. This yields the following:

dA/dt = kA --the rate of growth over time is k, some proportion [the growth rate] multiplied by A, the population.

This evaluates to our earlier equation A(t) = A₀e^kt.

For a growth model, k > 0, and in a decay model, k<0.