Question

Math help please

Answer 1

@Vocaloid or @dude please help w/ this whenever you get a chance

Answer 2

I think I remember answering this exact question last week.
Does it provide some options?

I wanna make sure we use the correct year for the base population value.
I think they want us to use 2005 for that value.

Answer 3

a ∙ bx = (550,521)(0.992)x


a ∙ bx = (550,521)(0.990)x


a ∙ bx = (550,521)(0.991)x


a ∙ bx = (550,521)(0.993)x

Answer 4

@Zepdrix these are the options

Answer 5

Wow those are all so close LOL
Within a thousandth of one another XD

Answer 6

Ok so assuming our "year zero" is 2005,
since that's the year we're basing the model from,

we get that a = 550521

and the years before 2005 can be thought of as negative values.
So in 2000, our x value is -5.

Answer 7

\[\large\rm f(x)=a\cdot b^x\]\[\large\rm f(x)=550521\cdot b^x\]

Answer 8

In 2000, x=-5 and our function (the population) is f(-5) = 571044.

Answer 9

\[\large\rm f(-5)=550521\cdot b^{-5}=571044\]

Answer 10

Solve for b.

Answer 11

Divide,\[\large\rm b^{-5}=\frac{571044}{550521}\]Take reciprocal of both sides to get rid of negative power,\[\large\rm b^5=\frac{550521}{571044}\]Finally, take fifth root of each side to remove fifth power,\[\large\rm b=\left(\frac{550521}{571044}\right)^{1/5}\]Giving us,\[\large\rm b\approx 0.992706495\]

Answer 12

So option D is probably what they're looking for, after rounding.