The following data represent the population of a countr

model that describes the population.

$($a$)$ Treating the year as the independent variable and the population as the

dependent variable, use a graphing utility to fit a logistic model from the data.

Find the values for $a,b$ and $c$ in a logistic model of the form $y=\frac{c}{1+a{e}^{-bx}}.$

$a=$

$($Use scientific notation. Round to five decimal places as needed.$)$

$b=$

$($Round to four decimal places as needed.$)$

$c=$

$($Round to one decimal place as needed.$)$

$($b$)$ Graph the data together with the logistic function found in part $($a$)$ on a scatter

diagram.

Which graph correctly illustrates the logistic growth model for this data?

A$.$

B$.$

C$.$

$($c$)$ Based on the logistic function found in part$($a$),$ what is the carrying capacity of the$$ country? Rounded to the nearest one.

$($d$)$ Use the function found in part$($a$)$ to predict the population of the country in $2007.$Rounded to the nearest one.

$($e$)$ Using the function from part$($a$),$ when will the$$ country's population be $500,000,000,$ sometime during the the year of $\_?$