A second population of ants also varies periodically with time. The population has the following properties:
Minimum population is 10 000 at t = 15 weeks
Maximum population is 40 000 at t = 5 weeks
It is assumed that the ant population follows a sine function of the form: y=AsinB(x+C)+D
Draw an $(x,y)$-figure with ticks at $0$, $5$, $\ldots$ on the $x$-axis and at $0$, $10$, $20$, $\ldots$ on the $y$-axis. Assuming that there are no maxima and minima between the two given data points sketch a sine arc that satisfies the conditions formulated in the word problem. Being a sine arc it has an obvious symmetry. You should then be able to adjust the constants in $$y=a\sin\bigl(\beta(x+c)\bigr)+ d$$ such that exactly the curve you have drawn results. Note that $a$ and $d$ are immediate. Furthermore you have to choose $\beta$ in such a way that between the $x$-ticks at $5$ and $15$ there is half a period. Etcetera.