The population (in millions) of a certain island can be approximated by the function p(x)=50(1.05)^x, where x is the number of years since 2000. in which year will the population reach 200 million? hint: an answer such as 2002.4 would represent 2002. a)2028 b)2015 c)2002 d)2066

a)2028

Step-by-step explanation:

Given: The population (in millions) of a certain island can be approximated by the function   , where x is the number of years since 2000.

To find the year in  in which year will the population reach 200 million, substitute p(x)=200, we get

Taking natural log on both the sides , we get

The year will be

Hence, in 2028  the population will reach 200 million.

answer: it's a

step-by-step explanation:

we have three similar triangles, because each has a right angle and shares an angle.   let's write the angles in order: opposite to short leg, long leg, hypotenuse.

cab similar to bad similar to cbd

or as ratios,

ca: ab: cb = ba: ad: bd = cb: bd: cd

we also know

ac = ad + cd

(ad+cd): ab: cb = ba: ad: bd = cb: bd: cd

(ad+cd)/cb=cb/cd

we have cb=6, ad=5 and seek x=cd.

we reject the negative root and conclude x=4

answer: 4