Question

There are currently 17 frogs in a (large) pond. The frog population grows exponentially, tripling every 6 days. How long will it take (in days) for there to be 130 frogs in the pond? Round your answer to the nearest hundredth.

Answer 1

Answer:

t=11,11 days

Step-by-step explanation:

F=frogs poblation, t=time, be the variables dF/dt = KF, dF/F=Kdt, integrating $\int\limits^ {} \, dF/F =K\int\limits^ {} \, dt$⇒ LnF=Kt+c,$F=ce^{Kt}$; Knowing t=0, F=17 and t=6 F=51 (tripling every 6 days (17*3)), $F=ce^{K0} = F=c=17; F=17e^{6K} =51$⇒$e^{6K} =51/17; K6=ln\frac{51}{17} ; K=ln\frac{51}{17}/6=0.183$, so $F=17e^{0,183t}$, now if F=130, t=? we have:

$130=17e^{0.183t} =e^{0.183t} =130/17; 0.183t=ln(130/17); t=ln(130/17)/0.183 = 11,11$