Question

A population of rabbits oscillates 19 above and below average during the year, hitting the lowest value in january. the average population starts at 650 rabbits and increases by 160 each year. find an equation for the population p in terms of the months since january t

Answer 1

Answer:

$p(t)=650+\frac{160}{12}t+19sin(\omega t)$

Step-by-step explanation:

The initial value of the population is 650

Each year the population increases 160

The population oscillates 19 above and below.

Due to this information you can assume that the function is:

$p(t)=650+\frac{160}{12}t+19sin(\omega t)$

where for t=0 p(t)=650

where t=12 160/12 (12) = 160

you can assume that the sinusoidal function has a period of one month. Thus, the population oscillates several times in one year with an amplitu of the oscillation of 19. The, w is:

$\omega (1)=2\pi\\\\\omega=2\pi$