3.1 Lesson 4 #1. The population of cyanobacteria in a pond is modeled by the function below, with t representing hours. After approximately how many hours
will this population reach 30,000 cyanobacteria?
P = 17,500e^.017t

30000=17500e^0.017t

e^0.017t=1.76

㏑1.76=0.017t

0.56=0.017t

t=33hours

option a, c,d are correct.

step-by-step explanation:

from the given figure, it is given that z is equidistant from the sides of the triangle rst, then from triangle tzb and triangle szb, we have

tz=sz(given)

bz=zb(common)

therefore, by rhs rule,δtzb ≅δszb

by cpctc, sz≅tz

also, from δctz and δasz,

tz=sz(given)

∠tcz=∠saz(90°)

by rhs rule, δctz ≅ δasz, therefore by cpctc, ∠ctz≅∠asz

also,from δasz and δzsb,

zs=sz(common)

∠zbs=∠saz=90°

by rhs rule, δasz ≅δzsb, therefore, by cpctc, ∠asz≅∠zsb

hence, option a, c,d are correct.